Projection display-use screen and projection display system optical system

ABSTRACT

To realize a diffusion film in which arbitrary control of the diffuse light intensity distribution characteristics, and an angular range of diffusion does not change with respect to an incoming light from a specific angular range and a light-outgoing direction converting element that is high in efficiency of conversion of the outgoing direction, and has no limit in the angle of conversion of the outgoing direction, and to provide a thin-model high-quality projection display using the same as a screen.

TECHNICAL FIELD

The present invention relates to a projection display screen and, morespecifically, to a projection display screen which is easy tomanufacture, is low in manufacturing cost, and has high-quality imagedisplay characteristics. The present invention also relates to a screenand an optical system for projection display system using a film with afunction of converting light-outgoing direction.

BACKGROUND ART

As a technology of the projection display screen in the related art,there exists a rear projection display screen including a diffusion film(for example, see Document 1, Okita et. al, Sumitomo Kagaku 1991-I, p.37-48) for diffusing incident light from a specific angular range into aspecific angular range (for example, see WO2004/034145).

This screen is different from a screen including a Fresnel lens, alenticular lens, and a diffusion film used generally in the related art,and has very effective advantages such that the structure is simple andthe cost can be reduced easily because it includes only the diffusionfilm for diffusing the incident light from the specific angular rangeinto the specific angular range as shown in FIG. 10, and that a diffuselight intensity distribution characteristics are substantially uniformfor the incident light from the specific angular range as shown in FIG.11 and hence variations in brightness in a screen is low.

On the other hand, in order to reduce the thickness of an optical systemfor a rear projection display system, as shown in FIG. 31 for example,it is necessary to arrange a projector 20 not on a screen optical axis10A, but at a position shifted from the screen optical axis 10A to causea projector light to enter into a screen 10 from an oblique direction.In general, most part of the projector light entered into the screen 10from the oblique direction does not diffuse in the front direction ofthe screen where an observer exists, but strongly in the direction ofstraight-ahead transmission of the projector light. Therefore, in orderto achieve the thickness reduction, it is very important to convert theout-going direction of the projector light incoming into the screen fromthe oblique direction into the front direction.

In order to achieve the conversion of direction of the projector lightas described above, as shown in FIG. 32 for example, a technology tocause the projector light 20A incoming from the oblique direction topass through a prism 30 to convert the outgoing direction by the use ofone or both of refraction 40 and total reflection 50 at an interface ofthe prism is known in the related art (for example, see Document 3,Shikama, S. et. al., SID '02 Digest, p. 1250-1253)

DISCLOSURE OF INVENTION Problems to be Solved by the Present Invention

In the projection display screen, it is very important that the diffuselight intensity distribution characteristics can be arbitrarilycontrolled. A diffusing model by diffraction of the incident light isproposed as regards a principle of the diffusion film which plays animportant role for realizing the characteristics in the above-describedscreen (see Document 1). However, the diffuse light intensitydistribution characteristics cannot be described clearly by using themodel, and hence the arbitrary control of the diffuse light intensitydistribution characteristics is not realized.

In the case of the screen using the prism as described above (SeeDocument 3), there are problems such that a stray light of the projectorlight may be generated at the complicated interface of the prism, whichmay lead to generation of a ghost on an image, and such that an externallight is reflected (rearward reflection) to the incident side (the sideof the observer) at the interface, which may results in lowering acontrast ratio. Furthermore, there are problems such that corners of theprism are rounded because of machining accuracy which may cause theprojector light to diffuse at the corners of the prism and hence theefficiency of conversion of the outgoing direction is lowered, therebyresulting in lowering of efficiency of usage of the projector light, andsuch that there exists a limit in angle of conversion of the outgoingdirection substantially because the efficiency of conversion of theoutgoing direction depends on the incident angle since the projectorlight falls mainly on the corners of the prism in the case of obliqueincidence.

In this case, the efficiency of conversion of the outgoing direction (orthe efficiency of conversion of the light-outgoing direction) representsa ratio in light-strength between a light incoming into thelight-outgoing direction conversion film from a certain angle or angularrange and a light outgoing at a certain angle or angular range, and theangles or angular ranges of incident light and outgoing light aregenerally determined by the incident angle of the projector light andthe screen diffusion characteristics. The angle of conversion of theoutgoing direction is an absolute value of a difference between thedirection of straight-ahead transmission and the outgoing direction fromthe light-outgoing direction converting element.

Accordingly, the object of the present invention is to realize adiffusion film in which the arbitrary control of the diffuse lightintensity distribution characteristics is possible, and the diffusingangular range is not varied with respect to an incident light from aspecific angular range, and to provide a high-quality projection displaysystem using the same as a screen. Furthermore, it is object of thepresent invention to realize a light-outgoing direction convertingelement that does not cause generation of ghost or lowering of contrastratio of images resulting from the complex interface, is high inefficiency of conversion of the outgoing direction, and has no limit inthe angle of conversion of the outgoing direction, and to provide athin-model high-quality projection display using the same as a screen.

MEANS FOR SOLVING THE PROBLEMS

After having devoted ourselves to study, in order to solve theabove-described problems, the Inventors obtained a structure of adiffusion film in which superior characteristics such as:

1) arbitrary control of the diffuse light intensity distributioncharacteristics is possible;

2) angular range of diffusion does not vary with respect to the incidentlight from a specific angular range;

3) blur of the incident light is low;

4) high transmission coefficient and low back scattering are realized;and

5) polarization of the incident light is maintained;

can be realized by using a principle of optical waveguide to cause thedirection of propagation of the incident light to be changed in flatplate waveguides laminated in layers in the direction in a plane.

Further, the inventors obtained a structure of a light-outgoingdirection converting film in which superior characteristics such as:

6) ghost of an image due to a stray light is not generated;

7) the amount of rearward reflection is small;

8) efficiency of conversion of the light-outgoing direction is high;

9) there is no limit in the angle of conversion of the outgoingdirection; and

10) polarization of an incident light is retained;

can be realized by changing the direction of propagation of incidentlight in a curved optical waveguide laminated in layers in the directionin the plane using a principle of the optical waveguide.

In other words, the present invention to be denoted by Claims 1 to 16 isas follows.

The present Claim 1 is a projection display screen having a diffusionfilm for diffusing light incoming from an angular range of diffusion ofan incident light into an angular range of diffusion of an outgoinglight, wherein the diffusion film comprises a structure in which aplurality of layers, each of which has a different refractive index fromthe adjacent layers, constituting a plurality of optical waveguides of astep index type forms a stripes arranged in the banded state in adirection in a film plane and extend in the direction of the layerinclination angle distributed substantially in a top hat shape within apredetermined angular range with respect to the direction of the filmthickness.

Claim 2 is a projection display screen having a diffusion film fordiffusing light incoming from an angular range of diffusion of anincident light into an angular range of diffusion of an outgoing light,wherein the diffusion film comprises a structure in which a plurality oflayers, each of which has a different refractive index from the adjacentlayers, constituting a plurality of optical waveguides of a step indextype forms a stripes arranged in a banded state in the direction in afilm plane, one or more peaks are included within a predeterminedangular range with respect to the direction of the film thickness, andthe plurality of layers extends in the direction of the layerinclination angle distributed substantially in a top hat shape exceptingsaid peaks within the angular range.

Claim 3 is, in Claim 1 or 2, the structure of the diffusion film is astructure in which the relation between a film thickness L and a maximumvalue of the width of the strip y_(max) is: L≧10×y_(max).

Claim 4 is a projection display screen having a diffusion film fordiffusing light incoming from an angular range of diffusion of anincident light into an angular range of diffusion of outgoing light,wherein the diffusion film comprises a structure in which a plurality oflayers constituting optical waveguides having a refractive indexdistribution that brings out a light-collecting property in thedirection of the layer thickness extends in the direction of the filmthickness or in the direction inclined from this direction with a layerlength distributed within a predetermined range substantially in the tophat shape in a portion in the direction of the film thickness.

Claim 5 is, in Claim 4, the structure of the diffusion film has therefractive index distribution of the optical waveguides of a gradientindex type, and a layer inclination angle θ, a maximum value L_(zmax)and a minimum value L_(zmin) of the layer length, and a pitch P of theoptical waveguides satisfies the following expression:L_(zmax)−L_(zmin)≧(P/2)×cos θ.

Claim 6 is a projection display screen having a diffusion film fordiffusing light incoming from an angular range of diffusion of anincident light into an angular range of diffusion of an outgoing light,wherein the diffusion film comprises a structure in which a portionhaving the same structure as the diffusion film according to any one ofClaims 1 to 3 and a portion having the same structure as the diffusionfilm according to Claim 4 or 5 are mixed in the direction of the filmthickness or in the direction in the film plane.

Claim 7 is a projection display screen having a diffusion film fordiffusing light incoming from an angular range of diffusion of anincident light into an angular range of diffusion of the outgoing light,wherein the diffusion film comprises a structure in which the structureof the diffusion film according to any one of the Claim 1 to 3 and thestructure of the diffusion film according to Claim 4 or 5 are fused witheach other.

Claim 8 is a screen using a film having a function of converting alight-outgoing direction comprising: a diffusion film for diffusinglight incoming from an angular range of diffusion of the incident lightinto an angular range of diffusion of an outgoing light; and alight-outgoing direction converting film for causing light incoming froman oblique direction to go out toward the front, wherein thelight-outgoing direction converting film comprises a structure in whicha plurality of layers, each of which has a different refractive indexfrom the adjacent layers, forming a plurality of step index type opticalwaveguides is arranged in a banded state in the direction of a filmplane, and extends so as to be bent with respect to the direction in thefilm thickness.

Claim 9 is a screen using a film having a function of converting alight-outgoing direction comprising: a diffusion film for diffusinglight incoming from an angular range of diffusion of the incident lightinto an angular range of diffusion of an outgoing light; and alight-outgoing direction converting film for causing light incoming froman oblique direction to go out toward the front, wherein thelight-outgoing direction converting film comprises a structure in whicha plurality of layers forming optical waveguides having a distributionof refractive indexes which brings out a light-collecting property inthe direction of the layer thickness is arranged in a banded state inthe direction in a film plane, and extends so as to be bent with respectto the direction of the film thickness.

Claim 10 is a screen using a film having a function of converting alight-outgoing direction comprising: a diffusion film for diffusinglight incoming from an angular range of diffusion of the incident lightinto an angular range of diffusion of an outgoing light; and alight-outgoing direction converting film for causing light incoming froman oblique direction to go out toward the front, wherein thelight-outgoing direction converting film comprises a structure in whichthe structure according to Claim 8 and the structure according to Claim9 are mixed in one or both of the film thickness direction and in thedirection in the film plane.

Claim 11 is, in any one of Claims 8 to 10 the angular range of diffusionof the incident light of the diffusing film matches the outgoing angularrange of the light-outgoing direction converting film.

Claim 12 is a screen having a light-outgoing directionconverting/diffusing film that causes incident light from an obliquedirection to diffuse and go out toward the front direction, wherein thelight-outgoing direction converting/diffusing film comprises a structurein which a plurality of layers, each of which has different refractiveindex from the adjacent layers, forming a plurality of step index typeoptical waveguides is arranged in a banded state in the direction in afilm plane, and extends so as to be bent with respect to the directionof the film thickness, and layer inclination angles are distributedsubstantially in a top hat shape.

Claim 13 is a screen having a light-outgoing directionconverting/diffusing film that causes incident light from an obliquedirection to diffuse and go out toward the front direction, wherein thelight-outgoing direction converting/diffusing film comprises a structurein which a plurality of layers forming optical waveguides having adistribution of refractive indexes which brings out a light-collectingproperty in the direction of the layer thickness is arranged in a bandedstate in the direction in a film plane, and extends so as to be bentwith respect to the direction of the film thickness, and the length ofthe layers are distributed substantially in a top hat shape.

Claim 14 is a screen having a light-outgoing directionconverting/diffusing film that causes incident light from an obliquedirection to diffuse and go out toward the front direction, wherein thelight-outgoing direction converting/diffusing film comprises a structurein which the structure according to Claim 12 and the structure accordingto Claim 13 are mixed in one or both of the film thickness direction andin the direction of the film plane, or a structure in which thestructure according to Claim 12 and the structure according to Claim 13are fused with each other.

Claim 15 is an optical system for projection display system comprising:a screen using a film having a function of converting a light-outgoingdirection according to any one of Claims 8 to 14, a projector whichemits an incident light to the screen, wherein a projector aperture andarrangement of the projector matches an angular range of incidence ofthe screen.

Claim 16 is, in Claim 15, further including a reflection mirror whichreflects the emitted light from the projector and causes the same toenter the screen, wherein the arrangement of the reflection mirrormatches the angular range of incidence of the screen.

EFFECTS OF THE PRESENT INVENTION

According to the present invention, Claims 1 to 7, the projectiondisplay screen having superior characteristics such as:

1) arbitrary control of the diffuse light intensity distributioncharacteristics is possible;

2) angular range of diffusion does not vary with respect to the incidentlight from a specific angular range;

3) blur of incident light is low;

4) high transmission coefficient and low back scattering are realized;and

5) polarization of the incident light is maintained; can be realized.

According to the present invention, Claims 8 to 14, a light-outgoingdirection converting film and a light-outgoing directionconverting/diffusing film which can realize superior characteristicssuch as:

6) ghost of an image due to a stray light is not generated;

7) the amount of rearward reflection is small;

8) efficiency of conversion of the light-outgoing direction is high;

9) there is no limit in the angle of conversion of the outgoingdirection; and

10) polarization of an incident light is retained; and a high-qualitythin-type projection display can be provided by using those films as ascreen and matching the arrangement of the projector and the reflectionmirror and the aperture of the projector and the aperture of the screen.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a pattern diagram showing an example of a film (1).

FIG. 2 is a pattern diagrams showing a layer inclination angle of thefilm (1).

FIG. 3 is a distribution chart showing a state in which the layerinclination angles of the film (1) are uniformly distributed within apredetermined range.

FIG. 4 is a distribution chart of the light intensity showing a relationbetween the incident angle and the outgoing angle of the film (1).

FIG. 5 is a pattern diagram showing an example of a film (2).

FIG. 6 is a cross-sectional view of a principal portion of FIG. 5 takenin the direction of film thickness and shown in an enlarged scale.

FIG. 7 is a drawing showing an example of refractive index distributionfunctions which brings out a light-collecting property in the directionof the layer thickness.

FIG. 8 is a distribution chart showing a state in which the layer lengthof the film (2) is distributed uniformly within a predetermined range.

FIG. 9 is a distribution chart of the light intensity showing a relationbetween the incident angle and the outgoing angle of the film (2).

FIG. 10 is a conceptual drawing of a rear projection display screenformed by a diffusion film for causing an incident light from a specificangular range to a specific angular range.

FIG. 11 is a distribution chart of the light intensity showing thediffusion characteristics of the screen shown in FIG. 10.

FIG. 12 is pattern diagrams; FIG. 12(a) shows an example of the film(3), (b) shows an example of the film (4), and (c) shows an example ofthe film (5).

FIG. 13 is a graph showing measurements of the distribution of the layerinclination angle of an incident side portion of the diffusion film usedin the present invention.

FIG. 14 is an explanatory drawing of derivation of a model expression ofthe film (1).

FIG. 15 is an explanatory drawing of derivation of the model expressionof the film (1).

FIG. 16 is a drawing showing a refractive index distribution of anoptical waveguide of the gradient index type.

FIG. 17 is a drawing showing light propagation within the opticalwaveguide of the gradient index type.

FIG. 18 is an explanatory drawing showing how to calculate the NA.

FIG. 19 is an explanatory drawing showing how to calculate the NA whenan optical axis of the optical waveguide of the gradient index type isinclined by an angle θ with respect to a normal line of the filmsurface.

FIG. 20 is an explanatory drawing showing a structure and a diffusioncharacteristic of the diffusion film used in a first embodiment.

FIG. 21 is an explanatory drawing showing a structure and a diffusioncharacteristic of the diffusion film used in a second embodiment.

FIG. 22 is a pattern diagram of a cross-sectional side view showing anexample of a screen of the present invention, and an example of anoptical system for rear projection display system using the same.

FIG. 23 is a pattern diagram showing an example of a light-outgoingdirection converting film in a case in which a curved optical waveguidearray is of a step index type.

FIG. 24 is an explanatory drawing of a coordinate of signs of angles anddirections of rotation.

FIG. 25 is a pattern diagram showing an example of the light-outgoingdirection converting film in a case in which the curved opticalwaveguide array is of a type having a distribution of refractive indexeswhich brings out a light-collecting property in the direction of thelayer thickness.

FIG. 26 is a pattern diagram showing (a) an example in which the opticalwaveguide array of the step index type and the optical waveguide arrayof the type having a distribution of refractive indexes which brings outa light-collecting property in the direction of the layer thickness aremixed in the direction of the film thickness, and (b) an example inwhich these arrays are mixed in the direction in a film plane.

FIG. 27 is an explanatory drawing showing relation between the anglerange corresponding to an NA and the diameter of a lens, the focallength, the imaging magnification, and the imaging position.

FIG. 28 is an explanatory drawing showing a step index optical waveguidebent structure model.

FIG. 29 is an explanatory drawing showing a state in which the model inFIG. 7 is formed in the film.

FIG. 30 is an explanatory drawing showing a state in which the model inFIG. 7 is formed in the film.

FIG. 31 is an explanatory drawing showing reduction of the thickness ofthe optical system employing projection display system.

FIG. 32 is a conceptual drawing of a related art using a prism.

FIG. 33 is (a) a side view and (b) a plan view showing an example of athin-type rear projection display system.

FIG. 34 is an explanatory drawing of a definition of a linear gradientindex optical waveguide.

FIG. 35 is an explanatory drawing showing derivation of an angle whichdetermines the NA in the linear gradient index optical waveguide.

FIG. 36 is an explanatory drawing showing a polygonal approximationmodel of a bent waveguide of a gradient index type.

FIG. 37 is an explanatory drawing showing a state in which the model inFIG. 36 is formed in the film.

FIG. 38 is an explanatory drawing of an analysis of an angle of anoptical axis that makes the NA symmetry on the upper side and the lowerside on the outgoing side of the bent waveguide of the gradient indextype.

FIG. 39 is an explanatory drawing of a radius of curvature of apolygonal approximation model of the bent waveguide of the gradientindex type.

FIG. 40 is an explanatory drawing showing a distribution of refractiveindexes which brings out a light-collecting property in the direction ofthe layer thickness other than the parabola type.

FIG. 41 is an explanatory drawing showing (a) a general outline of theoptical film used in a third embodiment and (b) a summary of experimentfor converting an outgoing direction using the bent waveguidemanufactured from the optical film.

FIG. 42 is an explanatory drawing showing a method of calculating thethickness of the film.

REFERENCE NUMERALS

-   -   1 layer (curved optical waveguide=bent waveguide)    -   1 _(A) layer (core)    -   1 _(B) layer (clad)    -   1 _(C) layer (layer having the distribution of refractive        indexes that brings out the light-collecting property in the        direction of the layer thickness)    -   2 light-outgoing direction converting film    -   2 _(X) remaining portion (film portion other than optical        waveguide)    -   3 diffusing film    -   4, 4 ₁, 4 ₂, 4 ₃, 4 ₄, 4 _(L) linear gradient index optical        waveguide    -   5, 6, 7, 8, 15, 16, 17, 18 light beam    -   9 optical film    -   9 ₁, 9 ₂ layer    -   9A optical film strip    -   10 screen    -   10A screen optical axis    -   11 light source    -   11 ₁ incident light    -   11 ₂ outgoing light    -   12 transparent medium    -   20 projector (optical engine)    -   20A projector light    -   21 object (image display panel)    -   30 prism    -   40 refraction    -   50 total reflection    -   51 film (1)    -   51 ₁ layer (core)    -   51 ₂ layer (clad)    -   52 film (2)    -   52 ₁ layer    -   53 film (3)    -   54 film (4)    -   53 ₁, 54 ₁ portion having the same structure as film (1)    -   53 ₂, 54 ₂ portion having the same structure as film (2)    -   55 film (5)    -   55 _(A) structure formed by fusing the structure of film (1) and        the structure of the film (2)    -   60 diffusion film (scattering film)    -   61 protective plate    -   62 projector    -   M1, M3 mirror    -   M2 non-spherical mirror

BEST MODE FOR CARRYING OUT THE INVENTION

In the present invention, an angle describing the optical system is, asshown in FIG. 24, such that an angle of a reference direction (forexample, a horizontal direction (z-direction)) is 0°, and an anglerotated leftward from the reference direction (counterclockwise) isrepresented as positive (+), and the angle rotated rightward (clockwise)is represented as negative (−)

About Claims 1 to 7

Firstly, a diffusion film (film (1)) according to Claims 1 to 3 will bedescribed.

FIG. 1 is a pattern diagram showing an example of a film (1). A film (1)51 can cause light incoming from an angular range of diffusion of theincident light θ_(in) to be diffused in an angular range of diffusion ofthe outgoing light θ_(out). A z-axis extends in the direction parallelto the direction of thickness L of the film (1) 51, and an x-axis and ay-axis orthogonal to each other in a plane perpendicular to the z-axis.

The film (1) 51 has a structure in which layers 51 ₁, 51 ₂ havingdifferent refractive indexes n₁, n₂ (n₁>n₂) from the adjacent layersform a stripe pattern (widths of the stripes y₁, y₂) arranged in onedirection in a film plane (xy-plane) alternately, and extend in adirection of an averaged inclination angle θ with respect to thedirection of the film thickness (z-direction). The conditions of thewidths of the stripes y₁, y₂ of the layers 51 ₁, 51 ₂ for causing theincident light to be diffused uniformly are represented as follows usingthe thickness L of the film (1) 51.L≧10×y ₁ , L≧10×y ₂

A layer inclination angle θ_(L) is defined by an inclination angle ofthe interface of the layer with respect to the z-axis, and varies withina range from a minimum inclination angle (θ−Δθ_(max)) to a maximuminclination angle (θ+Δθ_(max)) depending on the position in thedirection of the thickness of the film (1) 51 as shown in FIG. 2. Here,θ represents the average inclination angle, Δθ_(max) corresponds to ½ ofthe range of fluctuations of θ_(L).

Here, the conditions of the average inclination angle θ for causing thelight loss to be eliminated are represented as follows using therefractive index n₁.−sin⁻¹(1/n ₁)≦θ≦sin⁻¹(1/n ₁)

The respective layers in the film (1) 51 having the above-describedstructure are the same as in the optical waveguides of a step indextype. In these layers, the conditions of distribution of the layerinclination angle for causing the incident light to be diffuseduniformly is such that the distribution of the existentive probabilityof the layer inclination angle θ_(L) becomes the top hat shape(rectangular wave) when the layer inclination angle θ_(L) is within apredetermined range ((θ−Δθ_(max)) to (θ+Δθ_(max))) as shown in FIG. 3.Since it is difficult to achieve a complete top hat shape in reality, inthe present invention, the existential probability of the layerinclination angle in a predetermined range is defined to be distributedin substantially top hat shape while allowing the fluctuations in theexistential probability of the plateau section of the distribution curvewithin the range of ±40% of the average value and fluctuations in therespective domain widths at a riding edge and a falling edge at a ridingedge and a falling edge within the range of ±30% of the most-likelihoodhalf width of the entire distribution curve.

Also, there may be a case in which one or more peaks are mixed withinthe substantially top hat shaped distribution of the layer inclinationangle within a predetermined range in reality. However, since theadvantages of the present invention is not affected adversely if thepeak value of the existential probability does not exceed 1000% of theaverage value with the peaks excluded, such a case is also included inthe present invention. Preferably, the number of peaks is on the orderof five or less.

The uniformity of the diffuse light intensity depends not only on theexistential probability of the layer inclination angle, but also on thelength of the layer, and as the repetition of multiple reflections ofthe incident light increases with increase in length of the layer, moreuniform diffuse light intensity distribution characteristics isobtained. Therefore, a permissible range becomes wider than thatdescribed above in the case of a thick film having the film thickness Llarger than 50×y_(max). Here, y_(max) means either one of y₁ and y₂which is greater.

With the film (1) which satisfies the conditions described above, thelight incoming thereto from the angular range of diffusion of theincident light is diffused into the angular range of diffusion of theoutgoing light at substantially uniform light intensity.

Here, the angular range of diffusion of the incident light θ_(in) arerepresented by the following expression.Min[θ₁′,θ₁″,θ₂″,θ₂″]≦θ_(in)≦Max[θ₁′,θ₁″,θ₂′,θ₂″]θ₁′=sin⁻¹ [n ₁×sin{θ+Δθ_(max)+cos⁻¹(n ₂ /n ₁)}]  (1)θ₁″=sin⁻¹ [n ₁×sin{θ−Δθ_(max)+cos⁻¹(n ₂ /n ₁)}]  (2)θ₂′=−sin⁻¹ [n ₁×sin{−(θ+Δθ_(max))+cos⁻¹(n ₂ /n ₁)}]  (3)θ₂″=−sin⁻¹ [n ₁×sin{−(θ−Δθ_(max)(+cos⁻¹(n ₂ /n ₁)}]  (4)

Max{a, b} represents either one of a and b which is greater, and Min{a,b} represents either one of a and b which is smaller (hereinafter).

The angular range of diffusion of the outgoing light θ_(out) isrepresented as follows.Min[θ₁′,θ₁″,θ₂′,θ₂″]≦θ_(out)≦Max[θ₁′,θ₁″,θ₂′,θ₂″]  (5)

The above-described relation between the incident angle and the outgoingangle is shown in FIG. 4.

The above-described angles θ₁′, θ₁″, θ₂′, θ₂″ are derived as follows.

The film (1) has an optical waveguides of the step index type(hereinafter, referred to also as waveguides simply) being arranged inone-dimensional array and constitutes a layer structure, and thedirection of the layers are fluctuated. Assuming that the averagedirection of the layers is θ, and a model having fluctuations of±Δθ_(max) with respect to θ will be considered. When this model has auniform fluctuation in distribution of the layer inclination anglebetween (θ−Δθ_(max)) and (θ+Δθ_(max)), a light beam having an anglebetween a critical angle determined by (θ−Δθ_(max)) and a critical angledetermined by (θ+Δθ_(max)) repeats multiple reflections, and the angletherebetween are uniformly filled. In this mechanism, when thereflecting surface is not constituted by straight films but curves, anda plane wave (light beam) incoming from a certain direction is convertedinto a curved wave (spherical wave when the reflecting surface is formedof curves of second order), and when the angle exceeds the criticalangle, there is little reflection occurs any longer and diffusioncharacteristics of the top hat type which does not depend on thedirection of incidence, appear. The angle which determines the top hatcharacteristics is the critical angle determined by (θ−Δθ_(max)) and thecritical angle determined by (θ+Δθ_(max)).

There are two critical angles determined by the layer inclination angle(θ−Δθ_(max)) on the upper side and the lower side of the waveguide, andlikewise, there are two critical angles determined by the layerinclination angle (θ+Δθ_(max)) on the upper side and the lower side ofthe waveguide, and hence there exist four angles in total.

Derivation in the case of the layer inclination angle (θ+Δθ_(max)) willbe shown first. Assuming that n_(air) represents a refractive index ofair, n₁ represents a reflective index of core 51 ₁, n₂ represents arefractive index of clad 51 ₂ (n₁>n₂), when Snell's Law is applied tothe interface of the film on the incident side in FIG. 14,n _(air)×sin θ₁ ′=n ₁×sin θ₃  (A1)is obtained.

Then, the limit angle, that is, the critical angle at which the lightentered into the core 51 ₁ totally reflects on the upper interface withrespect to the clad 51 ₂ is given by the following expression.n ₁×sin{π/2−θ₃+(θ+Δθ_(max))}=n ₂×sin 90°  (A2)

From the expressions (A1) and (A2),θ₁′=sin⁻¹ [n ₁×sin{θ+Δθ_(max)+cos⁻¹(n ₂ /n ₁)}]  (A3)is obtained.

Subsequently, the angle which is determined by the lower interface ofthe waveguide will be derived. When Snell's Law is applied to the filminterface of the incident side in FIG. 15,n _(air)×sin(−θ₂′)=n ₁×sin(−θ₄)  (A4)is obtained.

Then, the limit angle (critical angle) at which the light entered intothe core 51 ₁ totally reflects on the lower interface with respect tothe clad 51 ₂ is given by the following expression. n₁×sin{π/2−(−θ₄)−(θ+Δθ_(max))}=n ₂×sin 90°  (A5)

From the expressions (A4), (A5),θ₂′=−sin⁻¹ [n ₁×sin{−(θ+Δθ_(max))+cos⁻¹(n ₂ /n ₁)}]  (A6)is obtained.

A method of derivation of the angles θ₁′ and θ₂′ which are determined bythe upper and lower core/clad interfaces in the case of the layerinclination angle (θ+Δθ_(max)) are described above.

Likewise, in the case of the layer inclination angle (θ−Δθ_(max)), theangles can be obtained by substituting (θ−Δθ_(max)) for (θ+Δθ_(max)) inthe expressions (A3) and (A6), and the expressions are as follows.θ₁″=sin⁻¹ [n ₁×sin{θ−Δθ_(max)+cos⁻¹(n ₂ /n ₁)}]  (A7)θ₂″=−sin⁻¹ [n ₁×sin{−(θ−Δθ_(max))+cos⁻¹(n ₂ /n ₁)}]  (A8)

Derivation of the four angles is now completed.

In the case of the film (1), the diffuse light intensity distributioncharacteristics of the outgoing light are determined by the existentialprobability of the layer inclination angle. In the example shown above,since the incident light is diffused in the light intensity distributionof the top hat type, the existential probability of the layerinclination angle is distributed in the top hat shape as shown in FIG.3. However, by varying the existential probability so as to bedistributed in substantially top hat shape (including the trapezoidalshape or the like) from the theory based on the same physical law, otherdesired diffuse light intensity distribution characteristics other thanthat of the top hat type (such as trapezoidal shape, Gaussiandistribution or the like) may be obtained.

In the example shown in FIGS. 1 to 2, the film in which the layerinclination angle is fluctuated only in the direction of the thicknessand the layer inclination angle is not fluctuated in the direction inthe plane has been described. However, by causing the layer inclinationangle to be fluctuated not only in the direction of thickness, but alsoin the direction in the plane, or by causing the layer inclination angleto be fluctuated only in the direction in the plane, and varying theexistential probability of the layer inclination angle according to thetheory based on the same physical law as the example shown above,desired diffuse light intensity distribution characteristics can beachieved.

Although the film surface is a planer surface in the example shown inFIG. 1 to FIG. 2, a case in which the film surface is a curved surfacecan be treated in the same manner by considering the curved surface tobe a group of minute planes.

Although there are two types of layers in the example in FIG. 1 to FIG.2, a structure having three or more types of layers may also be treatedin the same manner.

Subsequently, the diffusion film (film (2)) stated in claims 4 to 5 willbe described.

FIG. 5 is a pattern diagram showing an example of a film (2). Aprincipal portion of FIG. 5 is shown in an enlarged scale in FIG. 6. Afilm (2) 52 has a structure as shown below and hence the light incomingfrom the angular range of diffusion of the incident angle θ_(in) can bediffused into the angular range of diffusion of the outgoing lightθ_(out). The z-axis extends in the direction parallel to the directionof thickness L of the film (2) 52, and the x-axis and y-axis orthogonalto each other in the plane perpendicular to the z-axis.

The film (2) 52 has a structure in which a plurality of layers 52 ₁ of athickness b₁ which is partitioned by interfaces at an inclination angleθ with respect to the z-direction (θ which is the same sign as theaverage inclination angle in film (1) is used) are laminated in ay-direction at a portion in the direction of the film thickness. Thelayer 52 ₁ constitutes an optical waveguide having a refractive indexdistribution which brings out a light-collecting property in thedirection of the layer thickness. The portion of the film (2) other thanthe layer 52 ₁ has a constant refractive index n_(g). The conditions ofthe thickness b₁ of the layer for causing the incident light to bediffused uniformly are represented as follows using the thickness L ofthe film (2); L≧10×b₁.

The angle between the interfaces of the layer 52 ₁ (angle of the layer)θ with respect to the z-direction may be 0° (the extending direction ofthe layer 52 ₁ is perpendicular to the film plane). The layer length ofthe layer 52 ₁ (the length in the direction of the film thickness) isassumed to be L_(zmin) to L_(zmax). As shown in FIG. 6, axes obtained byrotating the z-axis and the y-axis about the x-axis by the angle θ arerepresented by an a-axis and a b-axis. In other words, the b-axisextends in parallel with the direction of the layer thickness, and thea-axis extends perpendicularly with respect to the b-axis and thex-axis.

There is an example of the refractive index distribution function whichbrings out the light-collecting property in the direction of the layerthickness as shown in FIG. 7. FIG. 7(a) shows a waveguide of a gradientindex type which has a refractive index distribution represented by thefollowing expression.n(b)=n ₁×(1−(A/2)×b ²)), −b ₁/2≦b≦b ₁/2, A: coefficient  (6)

Here, the conditions of the layer length for causing the incident lightto be diffused uniformly are represented by the following expressionsusing the layer inclination angle θ, the maximum value L_(zmax) and theminimum value L_(zmin) of the layer length, and the pitch P of theoptical waveguide.L _(zmax) −L _(zmin)≧(P/2)×cos θ  (7)P=2×π/√A  (8)A=(8/b ₁ ²)×(n ₁ −n ₂)/n ₁  (9)

At this time, it is ideal that the existential probability of the layerlength is distributed in the top hat shape as shown in FIG. 8. However,since it is difficult to achieve the complete top hat shape in reality,in the present invention, the existential probability of the layerlength in the range between L_(zmin) and L_(zmax) is defined to bedistributed in substantially top hat shape while allowing thefluctuations in the existential probability of the plateau section ofthe distribution curve within the range of ±40% of the average value andfluctuations in the domain width at the riding edge and the falling edgewithin the range of ±30% of the most-likelihood half width of the entiredistribution curve.

With the film (2) which satisfies the conditions described above, thelight incoming thereto from the angular range of diffusion of theincident light is diffused into the angular range of diffusion of theoutgoing light at a substantially uniform light intensity.

Here, the angular range of diffusion of the incident light θ_(in) isrepresented by the following expressions.θ_(NA2)≦θ_(in)≦θ_(NA1)  (10)θ_(NA1)=sin⁻¹ {n _(g)×sin(θ+θ_(g1))}  (11)θ_(NA2)=sin⁻¹ {n _(g)×sin(θ−θ_(g1))}  (12)sin θ_(g1)=(n ₁ /n _(g))×sin{tan⁻¹(n ₁ ×√A×b ₁/2)}  (13)

The angular range of diffusion of the outgoing light θ_(out) isrepresented as follows.θ_(NA2)≦θ_(out)≦θ_(NA1)  (14)

The above-described relation between the incident angle and the outgoingangle are shown in FIG. 9.

Since the light entered into an optical waveguide of the gradient indextype having the refractive index distribution in FIG. 7(a) propagateswithin the waveguide while changing the direction of travel in the rangeof:θ−tan⁻¹(n ₁ ×√A×b ₁/2)˜θ+tan⁻¹(n ₁ ×√A×b ₁/2)  (15)the diffuse light intensity distribution characteristics are determinedby the difference in the existential probability of the layer length.

As described above, in one mode of the film (2), since the opticalwaveguides of the gradient index type have an array structure, and thedirection of light propagation differs by the position in the directionof the length of the optical waveguide, the outgoing angle at theoutgoing end surface differs from waveguide to waveguide when there arefluctuations in length of the waveguides, which brings out the diffusionof light. Therefore, when variation in the direction of propagation inthe waveguide is linear with respect to the length of the waveguide, thediffusion characteristics of the top hat type is realized because of theuniform fluctuation in length.

Expressions for analyzing this mechanism will now be derived anddescribed.

First of all, attention is focused on one of the optical waveguides. Asshown in FIG. 16, it is assumed that the refractive index distributionfunction is given by the following quadratic function;n(r)=n ₁×(1−A/2×r ²)  (B1)symmetrically from the center of the optical waveguide.

Here, n₁ represents a refractive index on the center axis, A representsa distribution constant of the refractive index, and r represents adistance from the center. Assuming that a refractive index at positioncoordinates ±b₁/2 on both interfaces in the direction of the thicknessof the optical waveguide is n₂, the expression:A=(8/b ₁ ²)×(n ₁ −n ₂)/n ₁

As shown in FIG. 17, a z-axis is placed at the center of the opticalwaveguide of the gradient index type, and the position of the lightincident surface is assumed to be z=z₁. The distance from the z-axis isr. The distance from the z-axis at the position of the light incidentsurface is represented by r₁, the direction of the light beam in theoptical waveguide at this position is assumed to be r₁*=dr₁/dz=tan θ₁.Likewise, the position of the light outgoing surface is assumed to bez=z₂, and the distance from the z-axis is represented by r₂, and thedirection of the light beam in the optical waveguide at this position isassumed to be r₂*=dr₂/dz=tan θ₂.

Between the vector that represents the position and the direction of thelight beam on the light incident surface (input vector) [r₁, r₁*] andthe vector that represents the position and the direction of the lightbeam on the light outgoing surface (output vector) [r₂, r₂*], a relationas represented by the following expression (B2) is established.$\begin{matrix}\left\lbrack {{Expression}\quad 1} \right\rbrack & \quad \\{\begin{bmatrix}r_{2} \\r_{2}^{*}\end{bmatrix} = {\begin{bmatrix}{\cos\left\{ {\sqrt{A}\left( {z_{2} - z_{1}} \right)} \right\}} & \frac{\sin\left\{ {\sqrt{A}\left( {z_{2} - z_{1}} \right)} \right\}}{n_{1}\sqrt{A}} \\{{- n_{1}}\sqrt{A}\sin\left\{ {\sqrt{A}\left( {z_{2} - z_{1}} \right)} \right\}} & {\cos\left\{ {\sqrt{A}\left( {z_{2} - z_{1}} \right)} \right\}}\end{bmatrix}\begin{bmatrix}r_{1} \\r_{1}^{*}\end{bmatrix}}} & ({B2})\end{matrix}$

The expression (B2) means that being irrespective of the incidentposition r₁ of the light and the direction r₁* of the light beam at thisposition, distance from the z-axis and direction of the light beam at aposition is periodically restored to the initial state when traveled bya certain distance toward the z-axis. The distance in the direction ofthe z-axis which is restored periodically to the original state is apitch (P) of the optical waveguide of the gradient index type. For thesake of simplicity, when the position of the incident surface is assumedto be z₁=0, the expression (B3) is obtained from the expression (B2).$\begin{matrix}\left\lbrack {{Expression}\quad 2} \right\rbrack & \quad \\{\begin{bmatrix}r_{2} \\r_{2}^{*}\end{bmatrix} = {\begin{bmatrix}{\cos\left( {\sqrt{A}z_{2}} \right)} & \frac{\sin\left( {\sqrt{A}z_{2}} \right)}{n_{1}\sqrt{A}} \\{{- n_{1}}\sqrt{A}{\sin\left( {\sqrt{A}z_{2}} \right)}} & {\cos\left( {\sqrt{A}z_{2}} \right)}\end{bmatrix}\begin{bmatrix}r_{1} \\r_{1}^{*}\end{bmatrix}}} & ({B3})\end{matrix}$

The pitch (P) is obtained from the expression (B3). Since the componentsof 2 rows×2 columns in the expression (B3) are functions of sin and cos,when the √A×z₂ is changed by 2π, the position and the direction of thelight beam is restored to the initial state, and hence the pitch (P) canbe obtained from the following expression.√A×P=2π  (B4)Therefore;P=2π/√A  (B5)

Subsequently, the numerical aperture NA is calculated. The NA is givenby the largest angle out of the angles between the light beam which canbe propagated in the optical waveguide of the gradient index type andthe optical axis. In order to obtain the value of NA, as shown in FIG.18, the length z₂ of the optical waveguide of the gradient index type isrepresented by P/4, and the position of the incident light beam on theplane of z₁=0 is assumed to be r₁=b₁/2 (an end of the optical waveguidein the direction of thickness) and the direction of the light beam isassumed to be parallel with the optical axis (r₁*=dr₁/dz=tan θ₁=0).

Therefore, the input vector [r₁ r₁*] will be expressed by the followingexpression (B6). While the output vector [r₂ r₂*] will be expressed bythe following expression (B7), since r₂=0 as the length of the opticalwaveguide of the gradient index type z₂=P/4, and the incident light beamis parallel to the optical axis. By using the expression (B5): P=2π/√A,the expression: z₂=P/4 becomes the following expression (B8). Thensubstitution of the expressions (B6), (B7) and (B8) into the expression(B3), and arrangement thereof, will lead to the following expression(B9). $\begin{matrix}\left\lbrack {{Expression}\quad 3} \right\rbrack & \quad \\{\begin{bmatrix}r_{1} \\r_{1}^{*}\end{bmatrix} = \begin{bmatrix}\frac{b_{1}}{2} \\0\end{bmatrix}} & ({B6}) \\{\begin{bmatrix}r_{2} \\r_{2}^{*}\end{bmatrix} = \begin{bmatrix}0 \\r_{2}^{*}\end{bmatrix}} & ({B7}) \\{z_{2} = {\frac{P}{4} = \frac{\pi}{2\sqrt{A}}}} & ({B8}) \\{\begin{bmatrix}r_{2} \\r_{2}^{*}\end{bmatrix} = {\begin{bmatrix}0 & \frac{1}{n_{1}\sqrt{A}} \\{{- n_{1}}\sqrt{A}} & 0\end{bmatrix}\begin{bmatrix}\frac{b_{1}}{2} \\0\end{bmatrix}}} & ({B9})\end{matrix}$

The angle θ_(NA0) with respect to the optical axis on the outgoingsurface in the optical waveguide is given from the expression (B9).r ₂*=tan θ_(NA0) =−n ₁ ×√A×b ₁/2  (B10)

Therefore, from the expression (B10), assuming that θ_(NA0) is apositive value, θ_(NA0) is given by the following expression.θ_(NA0)=tan⁻¹(n ₁ ×√A×b ₁/2)  (B11)

The outgoing angle θ′_(NA0) of this light to the air layer satisfies therelation of the following expression by applying Snell's Law to theoutgoing surface on the optical axis.n _(air×sin θ′) _(NA0) =n ₁×sin θ_(NA0)  (B12)

Here, n_(air) represents the refractive index of air.

From the expressions (B11) and (B12), the NA of the optical waveguide ofthe gradient index type is given by the following expression.NA=sin θ′_(NA0)=(n ₁ /n _(air))×sin{tan⁻¹(n ₁ ×√A×b ₁/2)}  (B13)

Therefore, when fluctuations in the length of the optical waveguides ofthe gradient index type, L_(zmax)−L_(zmin) is larger than P/2 and thefluctuations are uniform, light diffusion of the top hat type is broughtout within the angle ±θ′_(NA0) of the NA given by the expression (B13).

The analysis described above is for the case in which the optical axisof the optical waveguide of the gradient index type coincides with thenormal line of the film plane.

Subsequently, analysis will be made for the case in which the opticalaxis is inclined by an angle θ with respect to the normal line of thefilm plane. As shown in FIG. 19, when there exists the optical waveguideof the gradient index type inclined by θ in the film, the optical systemin which the prisms of the same apex angle are arranged on the incidentside and the outgoing side of the optical waveguide on the oppositedirection is obtained. By obtaining the NA of this optical system, thetop hat characteristics of the film configured by the optical waveguideof the gradient index type inclined by θ can be described.

Since the optical system shown in FIG. 19 has the same structure on theincident side and the outgoing side, analysis is made on the outgoingside. θ_(NA0) in FIG. 19 is given by the expression (B11). When Snell'sLaw is applied to the optical axis of the optical waveguide of thegradient index type and the boundary portion with respect to the prismon the outgoing side, the following expression is obtained,n ₁×sin θ_(NA0) =n _(g)×sin θ_(g1)  (B14)

, where n_(g) represents the refractive index of the prism.

Subsequently, focusing attention on the light beam₁ which travelsupward, when Snell's law is applied to the boundary where this lightbeam goes out from the prism to the air layer, the following expressionis obtained.n _(g)×sin(θ+θ_(g1))=n _(air)×sin θ_(NA1)  (B15)

Subsequently, focusing attention on the light beam₂ which travelsdownward, when Snell's Law is applied to the boundary where it goes outfrom the prism to the air layer, the following expression is obtained.n _(g)×sin(θ−θ_(g1))=n _(air)×sin θ_(NA2)  (B16)

When sin θ_(g1) is obtained by substituting θ_(NA0) in the expression(B11) into the expression (B14), the following expression is obtained.sin θ_(g1)=(n ₁ /n _(g))×sin{tan⁻¹(n ₁ ×√A×b ₁/2)  (B17)

When θ_(NA1) and θ_(NA2) are obtained from the expressions (B15) and(B16) with n_(air)=1.0, the following expressions are obtainedrespectively.θ_(NA1)=sin⁻¹ >n _(g)×sin(θ+θ_(g1))}  (B18)θ_(NA2)=sin⁻¹ {n _(g)×sin(θ−θ_(g1))}  (B19)

Therefore, since this optical system has the same structure on theincident side and the outgoing side, the angles of the NA of the inputand output are represented by the following expressions.θ_(NA2)≦θ_(in)≦θ_(NA1)  (B20),θ_(NA2)≦θ_(out)≦θ_(NA1)  (B21)

The angle of meandering of light in the optical waveguide falls withinthe range between θ−θ_(NA0) and θ+θ_(NA0), since the optical axis isinclined by θ. When θ_(NA0) in the expression (B11) is substitutedthereto, the following expression is obtained.θ−tan⁻¹(n ₁ ×√A×b ₁/2)˜θ+tan⁻¹(n ₁ ×√A×b ₁/2)  (B22)

Since the optical axis is inclined by θ, the length of fluctuations ischanged to cos θ times of the length when θ=0°, and henceL_(zmax)−L_(zmin) is given by the following expression.L _(zmax) −L _(zmin)≧(P/2)×cos θ  (B24)

Derivation and description of the expression for the layers of the film(2) having the refractive index distribution in FIG. 7(a) is now ended.

On the other hand, the refractive index distribution in FIG. 7(b) isdifferent from that of the optical waveguide of the gradient index typeto some extent. However, since this can also bring out thelight-collecting property (the light-collecting property to keep theincident light within the layer) in the direction of the layerthickness, it can be treated in the same manner as the case of theoptical waveguide of the gradient index type, and the desired diffuselight intensity distribution characteristics can be obtained by varyingthe existential probability of the layer length.

Even in the case in which the optical waveguides of the gradient indextype having different refractive index distributions from point to pointare formed in the film, it can be treated in the same manner.

In the film (2), the diffuse light intensity distributioncharacteristics of the outgoing light is determined by the direction oflight propagation within the layer and the existential probability ofthe layer length. Although the existential probability of the layerlength is assumed to be distributed in the top hat shape in the exampleshown above in order to cause the incident light to be diffused in thedistribution of the light intensity of the top hat type, however, bycausing either one or both of the refractive index distribution withinthe layer and the existential probability according to the theory basedon the same physical laws, desired diffuse light intensity distributioncharacteristics other than those of the top hat type (for example, thetrapezoidal type, the Gaussian distribution, and so on) can also beobtained.

Although the film having no fluctuation in layer inclination angle isshown in FIGS. 5 to 6, desired diffuse light intensity distributioncharacteristics may be obtained by making the angle of layer inclinationin the direction in the plane fluctuated and changing the existentialprobability of the layer inclination angle as in the case of the film(1).

Although the surface of the film is planer in the example shown in FIG.5 and FIG. 6, even when the film surface is a curved surface, it can betreated in the same manner by considering it to be a group of minuteplanes.

Although the case in which the adjacent layers are in contact with eachother is shown in FIG. 5 and FIG. 6, it can be treated in the samemanner even when the adjacent layers are separated by some extent. Inthis case, however, part of the incident light is not propagated withinthe layer, and travels along the portion in the film (2) where therefractive index is constant (n_(g)), and hence the percentage of thelight which travels straight ahead is increased.

Although the film plane on one side is the incident side in FIG. 5 andFIG. 6, it can be treated in the same manner even when the film plane onthe opposite side is employed as the incident side.

Subsequently, diffusion film (film (3), film (4), and film (5)) statedin Claims 6 to 7 will be described. They have a structure in which thestructure of the film (1) and the structure of the film (2) arecombined.

FIG. 12(a) is a pattern diagram showing an example of the film (3). Asshown in the same drawing, a film (3) 53 has a structure in which a part53 ₁ having the same structure as the film (1) and a part 53 ₂ havingthe same structure as the film (2) are mixed in the direction of thefilm thickness.

FIG. 12(b) is a pattern diagram showing an example of the film (4). Asshown in the same drawing, a film (4) 54 has a structure in which a part54 ₁ having the same structure as the film (1), and a part 54 ₂ havingthe same structure as the film (2) are mixed in the direction of thefilm plane.

FIG. 12(c) is a pattern diagram showing an example of the film (5). Asshown in the same drawing, a film (5) 55 has the same structure 55 _(A)in which the structure of the film (1) and the structure of the film (2)are fused with each other.

In any of the diffusion films shown in FIG. 12, they can be treated asthe respective film (1) and film (2) in the decomposed state, and theangular range of diffusion of the incident light is derived bysuperimposing the respective films.

Claims 8 to 16

Subsequently, Claims 8 to 16 will be described.

In a rear projection display system (abbreviated as “rear pro”), inorder to reduce the thickness of the system, as shown in FIG. 33, forexample, an optical engine (projector) 20 is arranged on the lower sideof a screen 10, the direction of a light is changed by mirrors (mirrorsM1, M3, a non-spherical mirror M2) or the like, and images formed in anoblique direction from the lower side of the screen 10 with respect to anormal line of the screen are used. Therefore, since the diffusioncharacteristic in this structure is such that the center of a lightenergy is directed toward the upper side of the screen, a prism 30(prism sheet) is generally used to direct the center of light intensitytoward the normal line of the screen in the related art as shown in FIG.32.

However, when the prism sheet is used in the thin-type rear-pro, therearise problems such as fluctuation of characteristics due to joint usageof the refraction type and reflection type, and difficulty inmanufacture due to the difference in prism shape depending on thelocation to be provided.

In order to overcome such problems, the present invention employs alight-outgoing direction converting film 2 including a plurality oflayers 1 which constitute light waveguide arrays arranged in thedirection in the film plane in a striped state and extend so as to bebent with respect to the direction of the film thickness instead of theprism sheet in the related art as shown in FIG. 22. Reference numeral 3designates a diffusion film for causing a light incoming from an angularrange of diffusion of the incident light to be diffused into the angularrange of diffusion of the outgoing-light. The diffusion film 3 and thelight outgoing direction converting film 2 constitute the screen 10.

The optical waveguide 1 of the light-outgoing direction converting film2 is an optical waveguide of a step index type or an optical waveguideof a type having a distribution of refractive indexes which brings out alight-collecting property in the direction of the layer thickness (forexample, gradient index type).

FIG. 23 is a pattern diagram showing an example of a light-outgoingdirection converting film in a case in which a curved optical waveguidearray is of a step index type. Layers (cores) 1 _(A) having a refractiveindex n₁ which constitute the optical waveguides 1 and layers (clads) 1_(B) having a refractive index n₂ (n₁>n₂) are layered alternately in thedirection in the film plane. Reference numeral 2 _(X) designatesremaining portion (film portion other than the optical waveguide 1).Boundaries between the layers 1 _(A) and 1 _(B) are inclined by an angleof θ_(bend-in) on the incident side and by θ_(bend-out) on the outgoingside with respect to the normal line of the film plane. Such an opticalwaveguide of the step index type can be designed in such a manner thatan incident light beam 8 into the core 1 _(A) is totally reflected onthe layer boundary, while being propagated along a curve of the opticalwaveguide 1 in the core 1 _(A), and goes out with the direction of thecenter of the light intensity directed in a desired direction (forexample, in the direction of the normal line to the film plane)determined by θ_(bent-out).

FIG. 25 is a pattern diagram showing an example of the light-outgoingdirection conversion film in the case in which the curved opticalwaveguide array is of a type having a distribution of refractive indexeswhich brings out a light-collecting property in the direction of thelayer thickness. Layers 1 _(C) having the distribution of refractiveindexes that brings out the light-collecting property in the directionof the layer thickness are layered in the direction in the film plane toconstitute the optical waveguide array. Reference numeral 2 _(X)designates the remaining portion (film portion other than the opticalwaveguide 1). Boundaries of the layers 1 _(C) are inclined byθ_(bend-in) on the incident side and by θ_(bend-out) on the outgoingside with respect to the normal line to the film plane. The opticalwaveguide of the type having the distribution of refractive indexes thatbrings out the light-collecting property in the direction of the layerthickness can be designed in such a manner that the light beam 8 enteredinto the layer 1 _(C) is propagated in the layer 1 _(C) along the curveof the optical waveguide 1 while being refracted so as to draw a waveshape having an amplitude corresponding to the distance between thelayers and goes out with the direction of the center of the lightintensity directed in the desired direction (for example, the directionof the normal line to the film plane) determined by θ_(bend-out).

A single sheet of the light-outgoing direction converting film mayinclude only the optical waveguide of one of the step index type and thetype having the distribution of the refractive indexes which brings outthe light-collecting property in the direction of the layer thickness,or the optical waveguides of both types exist one or both of thedirection in the film plane and the direction of the film thickness in amixed manner. FIG. 26 show examples in which the optical waveguide arrayof the step index type and the optical waveguide array of the typehaving the distribution of refractive indexes which brings out thelight-collecting property in the direction of the layer thickness existin the direction of the film thickness in the mixed manner (a), andexist in the direction in the film plane in the mixed manner (b).

All the drawings and analysis disclosed in Claims 8 to 16 show examplesin which the remaining portion 2 _(X) having no layer formed thereinexists. However, it is a portion which does not contribute directly tothe light-outgoing direction converting property, and hence thelight-outgoing direction converting property can be brought out also bythe structure having no remaining portion 2 _(X) or having the same onlyon one side. This case can also be considered to be the same byconsidering the propagation of the light in the layers and calculatingthe refraction in the remaining portion 2 _(X) when going out therefromas in the case of an analysis shown below. Although the cross-section ofthe remaining portion 2 _(X) in the direction of the layer thickness isa triangular shape and one side thereof is assumed to be an airinterface of the film in the drawings, it can be considered to be thesame even when it has other structure from the same reasons (forexample, when the remaining portion 2 _(X) is significantly large andthere exists partly an range having no layer in the direction of thefilm thickness).

In the screen configured as described above, the light from the opticalengine can be reflected or refracted in the curved optical waveguide andthe direction of the center of the light intensity thereof can bedirected to the desired direction (for example, in the direction of thenormal line to the screen) determined by the θ_(bend-out). Accordingly,fluctuation of the characteristics due to the joint usage of therefracting type and the reflecting type and difficulty in manufacturedue to the difference in prism shape depending on the location to beprovided, as in the prism sheet in the related art, are diminished, andhence a light outgoing direction converting film which exerts superiorcharacteristics such as:

6) ghost of an image due to a stray light is not generated;

7) the amount of rearward reflection is small;

8) efficiency of conversion of the light-outgoing direction is high;

9) there is no limit in the angle of conversion of the outgoingdirection; and

10) polarization of an incident light is retained can be realized.

As a matter of course, if the outgoing angular range of thelight-outgoing direction converting film does not match the angularrange of diffusion of the incident light of the diffusion film, part ofthe projector light does not diffuse in the direction in which theobserver exists, and hence the usage efficiency of the projector lightis lowered. Therefore, it is preferable that these angular ranges match,and at least it is necessary that 50 percent of the outgoing angularrange θ_(out) of the light-outgoing direction converting film isincluded in the incident angular range of diffusion film θ_(bend-in).

Although the diffusion film to be used in combination with thelight-outgoing direction conversion film is not specifically limited,the diffusion film used in Claims 1 to 7 is preferable.

The light-outgoing direction converting film may be converted into thelight-outgoing direction converting/diffusing film having substantiallytop hat shaped diffused light-intensity characteristics by distributingthe layer inclination angle of the optical waveguide of the step indextype and/or the length of the optical waveguide layers of the typehaving the distribution of the refractive indexes which brings out thelight-collecting property in the direction of the layer thickness intosubstantially the top hat shape.

The light-outgoing direction converting/diffusing film corresponds tothe diffusion film used in Claims 1 to 7 with the optical waveguidestherein curved.

The single light-outgoing direction converting/diffusing film mayincludes only the optical waveguides of one of the step index type andthe type having the distribution of refractive indexes which brings outthe light-collecting property in the direction of the layer thickness ormay includes the optical waveguides of both types in one or both of thedirection in the film plane and the direction of the film thickness.

Further, the single light-outgoing direction converting/diffusing filmmay have a structure in which the optical waveguides of both typesdescribed above fused together. This structure has the distribution ofrefractive indexes in the layers is either one of a function of thedistribution of refractive indexes of the step index type or a functionof the distribution of refractive indexes which brings out thelight-collecting property in the direction of layer thickness, andincludes the curved layers in which both of the layer inclination angleand the layer length are distributed so as to be fluctuatedsubstantially in the top hat shape.

Since the light-outgoing converting/diffusing film has a function todiffuse the incident light with having bent in the optical waveguides,by using this film instead of the light-outgoing direction convertingfilm (the light-outgoing direction converting film without the diffusingfunction), it is not necessary to use an additional diffusing film, andhence the screen can be configured only with the light-outgoingdirection converting/diffusing film.

In the screen of Claims 8 to 14, the thickness of the respective layersforming the optical waveguides in the light-outgoing directionconverting film or the light-outgoing direction converting/diffusingfilm is preferably smaller than 500 μm considering the size of pixels ofthe image projected by the general projection display, since images ofhigh resolution cannot be propagated when it is too large.

The film plane of the light-outgoing direction converting film or thelight-outgoing direction converting/diffusing film is not limited to aplaner surface, and may be a curved surface. In the case of the curvedsurface, it can be handled in the same manner by considering it to be agroup of minute planes.

When constituting the optical system for projection display system usingthe screen of Claims 8 to 14, matching of an aperture (=NumericalAperture: abbreviated as NA) with the optical engine is important. TheNA of the optical engine is defined as NA=sin θ₂ where the angular rangeof a light beam incoming from behind the screen determined by the lensdiameter, the focal length, the image-forming magnification, and theimage-forming position of the optical engine 20 is assumed to be2θ₂(≡2×θ₂) as shown in FIG. 22 relating the case of the rear projectiondisplay, for example.

In the actual optical system for projection display system, the opticalelement such as a reflective mirror or a lens is arranged between theoptical engine and the screen in many cases as shown in FIG. 33, forexample. In such a case, the NA is defined in the same manner in thedrawing in which the optical system is converted into an opticallyequivalent mode using only one lens as shown in FIG. 22 or FIG. 27.

Assuming that a light emitted from an object (for example, an imagedisplay panel such as a liquid crystal or a DMD or the like in theprojection display) 21 having a length of S₁ placed at a distance “a”behind a lens of “d” in diameter and “f” in focal length as shown inFIG. 27 passes through the lens and forms an image at a distance “b”which satisfies the expression 1/a+1/b=1/f in front of the lens, thelength S₂ of the image satisfies the expression S₂/S₁=b/a, and assumingthat the distances from the center axis of the lens to the lower end andthe upper end of the image are l₁, l₂ respectively, and the anglesformed by straight lines connecting between the upper end of the lensand the lower end of the image, and between the lower end of the lensand the upper end of the image with respect to the center axis of thelens are θ₀, θ₁ respectively, the angular range 2θ₂ corresponding to theNA is represented by the following expression.2θ₂=θ₁−θ₀  (0-1)tan θ₁=(l ₂ +d/2)/b  (0-2)tan θ₀=(l ₁ −d/2)/b  (0-3)

If all the light in the angular range 2θ₂ cannot be bent in the curvedoptical waveguides (hereinafter, referred to as bent waveguides), theusage efficiency of the screen light is lowered. In addition, the lightleaked from the bent waveguides is led to lowering of the resolution ofthe image. Therefore, matching between the angular range 2θ₂ of theinput light beam from behind the screen and the angular rangecorresponding to the NA of the bent waveguides is very important interms of design of the optical system for projection display system.

Therefore, the theoretical derivation of the NA of the bent waveguideswill be described in detail below.

[NA of the Bent Waveguides of the Step Index Type]

FIG. 28 shows a curved structure model of the step index type opticalwaveguide. It has a structure in which the layers (core) 1 _(A) havingthe refractive index n₁ which constitute bent waveguides and the layers(clad) 1 _(B) having a refractive index n₂ which is smaller than n₁ arealternately layered. The core 1 _(A) is assumed to have the thicknessy₁, the center of curvature O, and the radius of curvature r₀ of theinterface surface on the inner peripheral side. In this model, in orderto make the NAs of the input and output easy to understand, linearstructures (L portions) of minute length Δz are added to an entrance andan exit of a bent structure (C portion) of the optical waveguides. Theexternal portion of the optical waveguide is an air layer having arefractive index n_(air).

The light beams 5, 6 are in modes which can be propagated in the core 1_(A) of the C portion. These two modes are modes which are propagated bybeing totally reflected at a critical angle θ_(C) on an interface of thecore 1 _(A) of the C portion with respect to the clad 1 _(B) on theouter peripheral side (outer interface), and at θ_(C)+θ_(r) on aninterface of the core 1 _(A) of the C portion with respect to the clad 1_(B) on the inner peripheral side (inner interface). A light beam 5 ispropagated by being totally reflected at the critical angle θ_(C) on theouter interface at the entrance and the exit of the C portion, and alight beam 6 is propagated by being totally reflected at a criticalangle of θ_(C)+θ_(r) on the inner interface at the entrance and the exitof the C portion.

When the light beam 5 is totally reflected at the entrance and the exitof the outer interface exactly at the critical angle, outgoing anglesinto the air layer are θ_(in1) and θ_(out1) in the drawing. When theposition is slightly shifted, since the total reflection is not effectedexactly at the entrance and the exit, the angles are −θ_(in1) and−θ_(out1). Therefore, the NA of the mode of the light beam 5 isdetermined by ±θ_(in1) and ±θ_(out1). When the same discussion is madefor the mode of the light beam 6, it can be said that the NA of the modeis determined by ±θ_(in2) and ±θ_(out2).

We now focus attention on the light beam 5. Although the drawing shows alight beam incoming at an angle of +θ_(in1), a light entering into theentrance on the outer interface at an angle of −θ_(in1) is considered(Δz is infinitely small). The light entering into the entrance on theouter interface can be propagated in the core of the C portion. However,when the incoming position is moved from the outer interface to theinner interface, the light beam is totally reflected at the criticalangle θ_(C) on the inner interface, and when it reaches the outerinterface, it enters into the outer interface at an angle smaller thanthe critical angle θ_(C), and hence the light does not totally reflectand refract into the clad. Therefore, in the case of the light beam 5,although the NA on the outer interface at the entrance and the exit aredetermined by ±θ_(in1) and ±θ_(out1), the NA is reduced as it approachesthe inner periphery, and at the position on the inner interface, theycoincide with the angles ±θ_(in2) and ±θ_(out2) which determine the NAof the light beam 6. Therefore, it can be said that the NA that allowssafe propagation through the waveguides of curved structure isdetermined by the angles ±θ_(in2) and ±θ_(out2) of the light beam 6.Therefore, the design of the screen is discussed by these angles.

Subsequently, referring to FIG. 28, these angles ±θ_(in2) and ±θ_(out2)will be derived. A sine theorem is applied to a triangle OAB in FIG. 28;The following expression is obtained.r ₀/sin θ_(C)=(r ₀ +y ₁)/sin{π−(θ_(C)+θ_(r))}  (1-1)

Since θ_(C) is the critical angle, using the refractive indexes n₁, n₂of the core and the clad, the following expression is obtained.θ_(C)=sin⁻¹(n ₂ /n ₁)  (1-2)

From the expressions (1-1), (1-2), the following expression is obtained.θ_(C)+θ_(r)=sin⁻¹{(n ₂ /n ₁)×(1+y ₁ /r ⁰)}  (1-3)

Therefore, Snell's Law of the following expression is established forthe interface between the air layer and the optical waveguide whereinthe light beam 6 is totally reflected at the point B.n _(air)×sin θ_(in2) =n ₁×sin{π/2−(θ_(C)+θ_(r))}  (1-4)

From the expressions (1-2), (1-4), θ_(in2)(=θ_(out2)) are given by thefollowing expression.θ_(in2)=θ_(out2)=sin⁻¹[(n ₁ /n _(air))×cos{sin⁻¹((n ₂ /n ₁)×(1+y ₁ /r₀))}]  (1-5)

Therefore, the input/output angle θ_(NAstep) with respect to the opticalaxis of the light which allows safe propagation without depending on theinput position in the curved structure model of the step index opticalwaveguide shown in FIG. 28 is given by the following expression from theexpression (1-5).−θ_(in2)(=−θ_(out2))≦θ_(NAstep)≦+θ_(in2)(=+θ_(out2))  (1-6)

Subsequently, an NA in the case where the model shown in FIG. 28 isformed in the film having a refractive index n_(g) is obtained. Sincethe output side is perpendicular to the film plane, the NA whose outputangle is ±θ_(out2) in the expression (1-5) is obtained. On the inputside, a prism (P portion) having the refractive index n_(g), whichcorresponds to the remaining portion 2 _(X) in FIG. 23, FIG. 25, andFIG. 26 is added. Such a state is shown in FIG. 29 and FIG. 30. Thelight beam 6 which is totally reflected on the inner interface at theentrance and the exit of the C portion is shown in FIG. 29, and a lightbeam 7 which is not totally reflected is shown in FIG. 30. For the sakeof easy understanding, L portions of Δz in length are added to theentrance and the exit of the C portion in FIG. 29. Actually, it may beconsidered as Δz→0.

The θ_(in4) in FIG. 29 is obtained in the following expression, byapplying Snell's Law on the interface between the air layer and the Pportion as regards the light beam 6.n _(air)×sin(−θ_(in4))=n _(g)×sin(θ_(bend)−θ_(in3))  (1-7)

Since θ_(in3) corresponds to θ_(in2) in the case in which n_(air) isreplaced by n_(g) in FIG. 28, by changing the n_(air) into n_(g) in theexpression (1-5), the following expression is obtained.θ_(in3)=sin⁻¹ [(n ₁ /n _(g))×cos(sin⁻¹((n ₂ /n ₁)×(1+y ₁ /r ₀))}]  (1-8)

From the expressions (1-7), (1-8),−θ_(in4)=sin⁻¹[(n _(g) /n _(air))×sin{−sin⁻¹((n ₁ /n _(g))×cos(sin⁻¹((n₂ /n ₁)×(1+y ₁ /r ₀))))+θ_(bend)}]  (1-9)is obtained.

Subsequently, θ_(in5) in FIG. 30 will be obtained. This can be obtainedsimply by changing the sign before θ_(bend) in the expressions (1-7) and(1-9), the following two expressions are established with correspondingto the expressions (1-7) and (1-9).n _(air)×sin(−θ_(in5))=n _(g)×sin(θ_(bend) −θ _(in3))  (1-10)θ_(in5)=sin⁻¹[(n _(g) /n _(air))×sin{sin⁻¹((n ₁ /n _(g))×cos(sin⁻¹((n ₂/n ₁)×(1+y ₁ /r ₀))))+θ_(bend)}]  (1-11)

Therefore, from the description above, the angle θ_(NAstepin) whichdetermines the NA on the incident side of the film as the curvedstructure model of the step index optical waveguide and the angleθ_(NAstepout) which determines the NA on the outgoing side thereof aregiven by the following two expressions.θ_(in4)≦θ_(NAstepin)≦θ_(in5)  (1-12)−θ_(out2)≦θ_(NAstepout)≦θ_(out2)  (1-13)

On the other hand, from FIG. 29 and FIG. 30, since −θ_(in4)≧−90°,θ_(in5)≦90°, from the expressions (1-9), (1-11), conditions of the layerinclination angle on the incident side θ_(bend) (hereinafter,represented as θ_(bend-in)) are represented by the following expression.|θ_(bend-in)|≦−sin⁻¹[(n ₁ /n _(g)]×cos{sin⁻¹((n ₂ /n ₁)×(2×R _(in) +y₁)/(2×R _(in) −y ₁))}]+sin⁻¹(n _(air) /n _(g))  (1-14)

-   -   where R_(in) represents a radius of curvature at the center        portion of the core thickness near the incoming surface        (=r₀+y₁/2).

In FIG. 28, if |θ_(C)+θ_(r)|>π/2, since the light beam 5 cannot totallyreflect on the inner interface, |θ_(C)+θ_(r)|≦π/2 is a prerequisite ofthe model, and from this condition and the expression (1-3),r₀≦n₂/(n₁−n₂)×y₁. Therefore, the radius of curvature at the centerportion of the core thickness of the curved waveguide must be at least aminimum radius of curvature R_(minstep) which is given by the followingexpression.R _(minstep) =n ₂/(n ₁ −n ₂)×y ₁ +y ₁/2=(n ₁ +n ₂)/(n ₁ −n ₂)×(y₁/2)  (1-16)

From the description above, in the case of the bent waveguides of thestep index type, a light entered into the bent waveguides at a certainincoming angle within the incoming angular range (θ_(in-min) toθ_(in-max)) is gradually changed in its direction of propagation in thebent waveguides and goes out at a certain outgoing angle within theoutgoing angular range (θ_(out-min) to θ_(out-max)). θ_(in-min),θ_(in-max), θ_(out-min), θ_(out-max) are given by the followingexpressions. $\begin{matrix}\left\lbrack {{Expression}\quad 4} \right\rbrack & \quad \\{\theta_{{in}\text{-}\min} = {\sin^{- 1}{\quad\left\lbrack {\frac{n_{g}}{n_{air}}\sin\left\{ {{- {\sin^{- 1}\left( {\frac{n_{1}}{n_{g}}{\cos\left( {\sin^{- 1}\left( {\frac{n_{2}}{n_{1}} \cdot \frac{{2R_{in}} + y_{1}}{{2R_{in}} - y_{1}}} \right)} \right)}} \right)}} + \theta_{{bend}\text{-}{in}}} \right\}} \right\rbrack}}} & \left( {1\text{-}17} \right) \\{\theta_{{in}\text{-}\max} = {\sin^{- 1}{\quad\left\lbrack {\frac{n_{g}}{n_{air}}\sin\left\{ {{\sin^{- 1}\left( {\frac{n_{1}}{n_{g}}{\cos\left( {\sin^{- 1}\left( {\frac{n_{2}}{n_{1}} \cdot \frac{{2R_{in}} + y_{1}}{{2R_{in}} - y_{1}}} \right)} \right)}} \right)} + \theta_{{bend}\text{-}{in}}} \right\}} \right\rbrack}}} & \left( {1\text{-}18} \right) \\{\theta_{{out}\text{-}\min} = {\sin^{- 1}{\quad\left\lbrack {\frac{n_{g}}{n_{air}}\sin\left\{ {{- {\sin^{- 1}\left( {\frac{n_{1}}{n_{g}}{\cos\left( {\sin^{- 1}\left( {\frac{n_{2}}{n_{1}} \cdot \frac{{2\quad R_{out}} + y_{1}}{{2\quad R_{out}} - y_{1}}} \right)} \right)}} \right)}} + \theta_{{bend}\text{-}{out}}} \right\}} \right\rbrack}}} & \left( {1\text{-}19} \right) \\{\theta_{{out}\text{-}\max} = {\sin^{- 1}{\quad\left\lbrack {\frac{n_{g}}{n_{air}}\sin\left\{ {{\sin^{- 1}\left( {\frac{n_{1}}{n_{g}}{\cos\left( {\sin^{- 1}\left( {\frac{n_{2}}{n_{1}} \cdot \frac{{2R_{out}} + y_{1}}{{2R_{out}} - y_{1}}} \right)} \right)}} \right)} + \theta_{{bend}\text{-}{out}}} \right\}} \right\rbrack}}} & \left( {1\text{-}20} \right)\end{matrix}$

In the models shown in FIG. 28 to FIG. 30, the layer interface from theentrance to the exit of the waveguides for all the optical paths arecurved lines having no abrupt change in angle. In this case, theincoming light is not diffused, and only the outgoing direction isconverted. On the other hand, according to the present invention, thelayer interface can be adapted to be a curved line whose angle isabruptly changed. In this case, the direction of reflection of theincoming light may be changed in the layer, so that the incoming lightcan be diffused while being changed in direction of travel. In thepresent invention, the phrase “the radius of curvature is fluctuatedfrom point to point to diffuse the incoming light” unless otherwisespecified indicates the case in which the layer inclination angle is acurved line whose angle is abruptly changed, and the term “abrupt changein the layer inclination angle” means the change in layer inclinationangle at least 0.01 deg./μm.

[NA of the Bent Waveguides of the Gradient Index Type]

According to the theoretical analysis of the inventors, when the curvedline of the bent waveguides of the gradient index type is approximatedby a polygonal line, the error of the radius of curvature by theapproximation is as small as 1.3% when the refractive index at thecenter portion of the width (layer thickness) of the bent waveguides is1.55, which is close to a core value of the general optical waveguides.Therefore, in the description below, the NA is derived by the polygonalapproximation model.

The linear portion in the polygonal approximation model is a lineargradient index optical waveguide 4, whose distribution of the refractiveindexes in the direction of the layer thickness as shown in FIG. 34 isrepresented by a curve of second order:n(r)=n ₁×(1−A/2×r ²)  (2-1)

where r represents a distance from the center of the layer thickness,and n₁ represents a refractive index on the center axis. A represents arefractive index distribution constant, and is represented byA=(8/y ₁ ²)×(n ₁ −n ₂)/n ₁  (2-2)by n₁, the layer thickness y₁, and the refractive index n₂ at the end ofthe layer thickness.

As shown in the drawings, assuming that the length of the waveguide isz, positions of the input light beam and the output light beam are r₁,r₂, directions of the light beam within the waveguide at the respectivepositions are r₁*=dr₁/dz=tan θ_(in), r₂*=dr₂/dz=tan θ_(out), thefollowing expression (2-3) is established between vectors [r₁, r₁*],[r₂, r₂*] representing the position and the direction of the input lightbeam and output light beam. $\begin{matrix}\left\lbrack {{Expression}\quad 5} \right\rbrack & \quad \\{\begin{bmatrix}r_{2} \\r_{2}^{*}\end{bmatrix} = {\begin{bmatrix}{\cos\left( {\sqrt{A}z} \right)} & \frac{\sin\left( {\sqrt{A}z} \right)}{n_{1}\sqrt{A}} \\{{- n_{1}}\sqrt{A}{\sin\left( {\sqrt{A}z} \right)}} & {\cos\left( {\sqrt{A}z} \right)}\end{bmatrix}\begin{bmatrix}r_{1} \\r_{1}^{*}\end{bmatrix}}} & \left( {2\text{-}3} \right)\end{matrix}$

In the expression (2-3), if the matrix term of 2×2 is a unit matrix, the[position, direction] vector is the same between the input light beamand the output light beam. The minimum solution of the length z at thistime is referred to as a pitch P of the waveguide, and factors of thematrix term are functions of sine and cosine. Therefore, the expressionP=2×π/√A  (2-4)is established.

The angle that determines the NA of the linear gradient index opticalwaveguide is given by the largest angle out of the angle between thelight beam that can be propagated in the waveguide and the optical axis(z-axis). As shown in FIG. 35, the largest angle corresponds to theangle θ_(NA0) between the output light beam and the optical axis(negative when y₁ is + and positive when y₁ is −) in the case where thelength of the waveguide is P/4, and the [position, direction] vectors ofthe input light beam and the output light beam are [±y₁/2, 0], [0, r₂*].The angle θ_(NA0) is obtained by substituting 0 for r₂, −y₁/2 for r₁, 0for r₁*, and P/4=π/(2×√A) for z into the expression (2-3), and obtainingthe value r₂*(=tan θ_(NA0)), which is represented by the expression;θ_(NA0)=tan⁻¹(n ₁ ×√A×y ₁/2)  (2-5)

FIG. 36 shows a polygonal approximation model. This is an approximationof the bent waveguide of the gradient index type obtained by the opticalwaveguides of a polygonal gradient index type in which a structure suchthat the above-described linear gradient index optical waveguide is bentby an angle θ_(NA0)/n (n is a real number equal to or larger than 0.5)at a position of the length P/2, and then by an angle θ_(NA0)/n at aposition proceeded by P/2 in the direction of the optical axis isrepeated. Light beams 15, 16, 17, 18 in the drawing indicate modes ofthe representative light beam which can be propagated in the polygonaloptical waveguide. When n is smaller than 0.5, since the light goes outfrom the waveguide, it is excluded from the object of the model.

The light beam 17 is a light incoming in parallel with the optical axisof the first linear gradient index optical waveguide 4 ₁ (hereinafter,referred to as the optical waveguide 4 ₁) to a position of the opticalaxis, and this light travels straight ahead in the optical waveguide 4₁, and then enters into the second linear gradient index opticalwaveguide 4 ₂ (hereinafter, referred to as the optical waveguide 4 ₂)which is inclined by −θ_(NA0)/n at a position advanced by P/2.Therefore, the incident angle into the optical waveguide 4 ₂ isθ_(NA0)/n. Since the lengths of the respective linear gradient indexoptical waveguides are P/2, the outgoing angle of the optical waveguide4 ₂ is −θ_(NA0)/n with respect to the optical axis of the opticalwaveguide 4 ₂. Since the third linear gradient index optical waveguide 4₃ (hereinafter, referred to as the optical waveguide 4 ₃) is inclined by−θ_(NA0)/n with respect to the second optical waveguide 4 ₂, theincident angle of the light beam 7 is 0°, and hence the light beam 17travels straight ahead in the linear gradient index optical waveguide ofthe odd number sequence, and changes the direction of travel and curvedfrom the incident angle: +θ_(NA0)/n to the outgoing angle: −θ_(NA0)/n inthe linear gradient index optical waveguide of the even number sequence.On the other hand, the light beam 16 shows a mode in which the state inthe linear gradient index optical waveguides of the odd number sequenceand the even number sequence of the light beam 17 are exchanged.

The light beams which determine the NA of the polygonal gradient indexoptical waveguide are the light beam 15 and the light beam 18.

The light beam 15 is a light beam of the maximum possible incident anglewhich can be propagated in the optical waveguide 4 ₁. Therefore, theincident angle into the waveguide of the optical waveguide 4 ₁ isθ_(NA0). Since the lengths of the respective linear gradient indexoptical waveguides are P/2, the outgoing angle of the light beam 15 fromthe optical waveguide 4 ₁ is −θ_(NA0). Since the optical waveguide 4 ₂is inclined by −θ_(NA0)/n with respect to the optical waveguide 4 ₁, theincoming angle of the light beam 15 with respect to the optical axis ofthe optical waveguide 4 ₂ is −(1−1/n)×θ_(NA0). Since the absolute valueof the incident angle: |(1−1/n)×θ_(NA0)| is smaller than θ_(NA0), thelight beam 15 can be propagated within the optical waveguide 4 ₂. Sincethe length of the optical waveguide 4 ₂ is also P/2, the outgoing anglewith respect to the optical axis of the optical waveguide 4 ₂ is(1−1/n)×θ_(NA0). Since the optical waveguide 4 ₃ of the next sequence isinclined by −θ_(NA0)/n with respect to the optical waveguide 4 ₂, theincident angle of the light beam 15 with respect to the opticalwaveguide 4 ₃ is θ_(NA0), which is the same light propagation state inthe optical waveguide 4 ₁. Therefore, the light beam 15 is a mode inwhich the direction is changed from the incident angle: θ_(NA0) to theoutgoing angle: −θ_(NA0) in the linear gradient index optical waveguideof the odd number sequence, and from the incident angle:−(1−1/n)×θ_(NA0) to the outgoing angle: (1−1/n)×θ_(NA0) in the lineargradient index optical waveguide of the even number sequence, beforepropagation. In other words, the mode shown in conjunction with thelight beam 15 is a mode of the maximum possible incident angle which canbe propagated within the linear gradient index optical waveguide of theodd number sequence. On the other hand, the light beam 18 represents amode in which the state in the linear gradient index optical waveguidesof the odd number sequence and the even number sequence of the lightbeam 15 are exchanged. Therefore, the NA of the polygonal gradient indexoptical waveguide is determined by an angle between the incident angleand the outgoing angle of the light beam 15 and by an angle between theincident angle and the outgoing angle of the light beam 18.

Subsequently, the NA will be obtained. Assuming that the number of thelinear gradient index optical waveguides which constitute the polygonalmodel is a natural number k, an optical axis of the k^(th) lineargradient index optical waveguide is bent by an angle θ_(bend), which isrepresented by the following expression, with respect to that of thefirst linear gradient index optical waveguide.θ_(bend)=−(k−1)×θ_(NA0) /n  (2-6)

The angle θ_(NA0)(k) which determines the NA of the outgoing side in thek^(th) linear gradient index optical waveguide is given by followingexpression, from FIG. 36,θ_(bend)−θ_(NA0)≦θ_(NA0)(k)≦θ_(bend)+(1−1/n)×θ_(NA0)  (2-7)and the following expression is obtained by substituting the expression(2-6) into about expression (2-7).−θ_(NA0) /n×(k+n−1)≦θ_(NA0)(k)≦−θ_(NA0) /n×(k−n)  (2-8)

Since the natural number k exists in the angle represented by theexpressions (2-6), (2-7), and (2-8), it is a discrete angle definition.However, the polygonal approximation model in FIG. 36 is anapproximation of the bent waveguide existing in the actual film.Therefore, even when the entire model is continuously rotated about thecenter of the curvature of the polygonal approximation model in FIG. 36,the NA of the model does not change, and the NA is determined by theradius of curvature and the refractive index distribution function n(r)represented by the expression (2-1).

Therefore, θ_(bend) in the expression (2-7) can be treated as acontinuous value, not as a discrete value. An angle θ_(NA1) whichdetermines the NA in the optical waveguide of the polygonalapproximation model in the case where the θ_(bend) is treated as thecontinuous value is given by the following expression.θ_(bend)−θ_(NA0)≦θ_(NA1)≦θ_(bend)+(1−1/n)×θ_(NA0)  (2-9)

When the model in FIG. 36 is formed in the film, as shown in FIG. 37,the prism (P portion) having a refractive index n_(g) and apex angleθ_(bend) which correspond to the remaining portion 2 _(X) in FIG. 23,FIG. 25, and FIG. 26 are added to the outgoing portion on the rightside.

When Snell's Law is applied to the interface between the outgoing end ofthe waveguide 4 ₄ and the P portion and the interface between the Pportion and the air layer (refractive index: n_(air)) for the light beam18, the following expressions (2-10) and (2-11) are obtainedrespectively.n ₁×sin θ_(NA0) =n _(g)×sin θ_(ng1)  (2-10)n _(g)×sin(θ_(bend)+θ_(ng1))=n _(air)×sin θ_(out1)  (2-11)

From the expressions (2-10), (2-11), the θ_(out1) is obtained by thefollowing expression.θ_(out1)=sin⁻¹ [n _(g) /n _(air)×sin{θ_(bend)+sin⁻¹(n ₁ /n _(g)×sinθ_(NA0))}]  (2-12)

When performing the same analysis for the light beam 15, the followingtwo expressions are established.n ₁×sin{(1−1/n)×θ_(NA0) }=n _(g)×sin θ_(ng2)  (2-13)n _(g)×sin(θ_(bend)−θ_(ng2))=n _(air)×sin θ_(out2)  (2-14)

From the expressions (2-13) and (2-14), θ_(out2) is given by thefollowing expression.θ_(out2)=sin⁻¹ [n _(g) /n _(air)×sin{θ_(bend)−sin⁻¹(n ₁ /n_(g)×sin((1−1/n)×θ_(NA0)))}]  (2-15)

From the expressions (2-12) and (2-15), the NA on the outgoing side isdetermined by the following θ_(NAout).−θ_(out2)≦θ_(NAout)≦−θ_(NAout)  (2-16)

The NA on the incident side is θ_(bend)=0° in the expressions (2-12) and(2-15), and when θ_(out1) in the expression (2-12) is changed intoθ_(in1), and θ_(out2) in the expression (2-15) is changed into θ_(in2),the following two expressions are established.θ_(in1)=sin⁻¹(n ₁ /n _(air)×sin θ_(NA0))  (2-17)θ_(in2)=sin⁻¹ {n ₁ /n _(air)×−sin((1−1/n)×θ_(NA0))}  (2-18)

From the expressions (2-12) and (2-15), the NA on the incident side isdetermined by θ_(NAin) in the following expression.θ_(in2)≦θ_(NAin)≦θ_(in1)  (2-19)

In the model shown in FIG. 36, although the input and output angles ofthe light are opposite to the case of the rear projection display systemin FIG. 22, by changing the lower case “out” attached to the angle θ inthe expressions (2-12), (2-15) and (2-16) into “in”, the following threeexpressions in which the angle on the incident side matches the systemin FIG. 22 are established.θ_(in1)=sin⁻¹ [n _(g) /n _(air)×sin{θ_(bend)+sin⁻¹(n ₁ /n _(g)×sinθ_(NA0))}]  (2-12A)θ_(in2)=sin⁻¹ [n _(g) /n _(air)×sin{θ_(bend)−sin⁻¹(n ₁ /n_(g)×sin((1−1/n)×θ_(NA0)))}]  (2-15A)θ_(in2)≦θ_(NAin)≦θ_(in1)  (2-16A)

On the outgoing side, the following three expressions which match thesystem in FIG. 22 are established from the expressions (2-17), (2-18)and (2-19).θ_(out1)=−sin⁻¹(n ₁ /n _(air)×sin θ_(NA0))  (2-17A)θ_(out2)=sin⁻¹ {n ₁ /n _(air)×sin((1−1/n)×θ_(NA0))}  (2-18A)θ_(out1)≦θ_(NAout)≦θ_(out2)  (2-19A)

The expression (2-19A) represents the fact that when the optical axis ofthe optical waveguide is bent to the direction of the normal line of thescreen, the NA on the outgoing side becomes asymmetry. Therefore,subsequently, the angle θ_(axis) of the optical axis of the opticalwaveguide on the outgoing side for causing the NA to be symmetry on theupper side and lower side on the outgoing side is obtained by analysis.

FIG. 38 shows an end portion of the last optical waveguide (lineargradient index optical waveguide) 4 _(L) on the outgoing side, which isended by an angle θ_(axis) of optical axis. The output NA is determinedby the angle between the light beams 15 and 18. Therefore, the value ofθ_(axis) when θ_(out3)=θ_(out4) is established in the drawingcorresponds to the angle of the optical axis to be obtained.

θ_(out3) will be obtained by the expression (2-22) from the expression(2-20) which is established on the interface between the outgoingsurface of the optical waveguide and the P portion and the expression(2-21) established on the interface between the P portion and the airlayer for the light beam 18.n ₁×sin θ_(NA0) =n _(g)×sin θ_(ng3)  (2-20)n _(g)×sin(θ_(ng3)−θ_(axis))=n _(air)×sin θout3  (2-21)θ_(out3)=sin⁻¹ [n _(g) /n _(air)×sin{sin⁻¹(n ₁ /n _(g)×sinθ_(NA0))−θ_(axis)}]  (2-22)

θ_(out4) is obtained from the expression (2-25) from the expression(2-23) established on the interface between the outgoing surface of theoptical waveguide and the P portion and the expression (2-24)established on the interface between the P portion and the air layer forthe light beam 15.n ₁×sin{(1−1/n)×θ_(NA0) }=n _(g)×sin θ_(ng4)  (2-23)n _(g)×sin(θ_(ng4)+θ_(axis))=n _(air)×sin θ_(out4)  (2-24)θ_(out4)=sin⁻¹ [n _(g) /n _(air)×sin{sin⁻¹(n ₁ /n_(g)×sin((1−1/n)×θ_(NA0)))+θ_(axis)}]  (2-25)

Therefore, from the expressions (2-22)=(2-25), θ_(axis) to be obtainedis given by the following expression.θ_(axis)=½×[sin⁻¹(n ₁ /n _(g)×sin θ_(NA0))−sin⁻¹(n ₁ /n_(g)×sin((1−1/n)×θ_(NA0)))]  (2-26)

An angle which determines the NA on the outgoing side under theestablishment of the expression (2-26) can be obtained by the followingexpression, by substituting the expression (2-26) into the expression(2-22) or the expression (2-25), herein an angle to be obtained isθ′_(out3)=θ′_(out4).θ′_(out3)=θ′_(out4)=sin⁻¹ [n _(g) /n _(air)×sin{½×sin⁻¹(n ₁ /n_(g)×sin((1−1/n)×θ_(NA0)))+½×sin⁻¹(n ₁ /n _(g)×sin θ_(NA0))}]  (2-27)

Therefore, from the expression (2-27), an angle which determines the NAon the outgoing side which is symmetry on the upper and lower sides isobtained by the following expression.−θ′_(out3)≦θ_(NAout)≦θ′_(out3)  (2-28)

Subsequently, the radius of curvature of this model is derived. As shownin FIG. 39, in this polygonal approximation model, the center ofcurvature is an intersection O of perpendicular bisectors of therespective segments having a length P/2 of the linear gradient indexoptical waveguides 4 ₁, 4 ₂, 4 ₃, . . . , and a radius of curvature R(R=r₀+y₁/2 from the same drawing) is a distance from the center ofcurvature O to the center points of the length and the thickness of therespective optical waveguides 4 ₁, 4 ₂, 4 ₃, . . . In the same drawing,when attention is focused on a right-angled triangle having the apexangle θ_(NA0)/(2×n), the following expression is established.tan(θ_(NA0)/(2×n))=(P/4)/(r ₀ +y ₁/2)  (2-29)

From the expression (2-29), the radius of curvature R is given by thefollowing expression.R=r ₀ +y ₁/2=(P/4)/tan(θ_(NA0)/(2×n))  (2-30)

In other words, when θ_(NA0) and P of the linear gradient index opticalwaveguide which are of the polygonal approximation model are obtained,and n (real number equal to or larger than 0.5) that determines the bentangle (bending extent) is determined, the radius of curvature isdetermined by the expression (2-30). The minimum radius of curvatureR_(min) is obtained by the following expression, when n=0.5, and isgiven by an expression obtained by substituting 0.5 for n in theexpression (2-30) and the expressions (2-4) and (2-5).R _(min)=π/(n ₁ ×A×y ₁)  (2-31)

In this case, the error of the polygonal approximation model becomes themaximum value. On the other hand, although detailed description of theprocess of derivation is omitted, the minimum radius of curvatureR′_(min) of the optical waveguides of the gradient index type (curvedstructure model) having the same thickness and distribution ofrefractive index is given by the following expression.R′ _(min)=2/(A×y ₁)  (2-32)

From the expressions (2-31) and (2-32), an error factor between theR′_(min) (corresponding to a rigorous solution) and the R_(min)(corresponding to an approximated solution) is π/(2×n₁), and when 1.55,which is close to the core value of the general optical waveguide, issubstituted for n₁, 1.0134 is obtained as the value of the error factor.Therefore, the error of the approximated solution with respect to therigorous solution is within the 1.3% at the maximum, and hence thepolygonal approximation model can be said to be sufficiently goodapproximation of the curved structure model.

Since the incident angle of the light is within the range between −90°and 90° with respect to the normal line to the film plane, θ_(in2)≧−90°and θ_(in1)≦90° are established in the expression (2-16A). From theseconstraints and the expressions (2-12A) and (2-15A), a condition of thelayer inclination angle near the incident surface θ_(bend-in) areexpressed by the following expression using the radius of curvature ofthe layer near the incident surface R_(in), the angle of propagation inthe layer θ_(NA0), and the pitch P of the light propagation.θ_(bend-in-min)≦θ_(bend-in)≦θ_(bend-in-max)  (2-33)θ_(bend-in-min)=sin⁻¹ {n ₁ /n _(g)×sin(θ_(NA0)−2×tan⁻¹(P/(4×R_(in))))}−sin⁻¹(n _(air) /n _(g))  (2-34)θ_(bent-in-max)=−sin⁻¹(n ₁ /n _(g)×sin θ_(NA0))+sin⁻¹(n _(air) /n_(g))  (2-35)

Since the outgoing angle of the light is also within the range between−90° and 90° with respect to the normal line to the film plane,θ_(out2)≧−90° and θ_(out1)≦90° are established in the expression (2-16).From these constraints and the expressions (2-12) and (2-15), acondition of the layer inclination angle near the incident surfaceθ_(bend-out) are expressed by the following expression using the radiusof curvature of the layer near the incident surface R_(out), the angleof propagation in the layer θ_(NA0), and the pitch P of the lightpropagation.−θ_(bend-out-min)≦θ_(bend-out)≦θ_(bend-out-max)  (2-36)θ_(bend-out-min)=sin⁻¹ {n ₁ /n _(g)sin(θ_(NA0)−2×tan⁻¹(P/(4×R_(out))))}−sin⁻¹(n _(air) /n _(g))  (2-37)θ_(bent-out-max)=−sin⁻¹(n ₁ /n _(g)×sin θ_(NA0))+sin⁻¹(n _(air) /n_(g))  (2-38)

The lowest limit of the radius of curvature of the layer in the film isthe value of the expression (2-32).

From the description above, in the bent waveguide of the gradient indextype, the light incoming into the bent waveguide at a certain incidentangle within the range of the incident angle (θ_(in-min) to θ_(in-max))is changed gradually in the direction of propagation within the bentwaveguide, and goes out at a certain outgoing angle within the range ofthe outgoing angle (θ_(out-min) to θ_(out-max)). The θ_(in-min),θ_(in-max), θ_(out-min), θ_(out-max) are given by the followingexpression. $\begin{matrix}\left\lbrack {{Expression}\quad 6} \right\rbrack & \quad \\{\theta_{{in}\text{-}\min} = {\sin^{- 1}\left\lbrack {\frac{n_{g}}{n_{air}}\sin\left\{ {{- {\sin^{- 1}\left( {\frac{n_{1}}{n_{g}}{\sin\left( {\theta_{{NA}\quad 0} - {2\tan^{- 1}\frac{P}{4R_{in}}}} \right)}} \right)}} + \theta_{{bend}\text{-}{in}}} \right\}} \right\rbrack}} & \left( {2\text{-}39} \right) \\{\theta_{{in}\text{-}\max} = {\sin^{- 1}\left\lbrack {\frac{n_{g}}{n_{air}}\sin\left\{ {\theta_{{bend}\text{-}{in}} + {\sin^{- 1}\left( {\frac{n_{1}}{n_{g}}\sin\quad\theta_{{NA}\quad 0}} \right)}} \right\}} \right\rbrack}} & \left( {2\text{-}40} \right) \\{\theta_{{out}\text{-}\min} = {\sin^{- 1}\left\lbrack {\frac{n_{g}}{n_{air}}\sin\left\{ {{- {\sin^{- 1}\left( {\frac{n_{1}}{n_{g}}{\sin\left( {\theta_{{NA}\quad 0} - {2\tan^{- 1}\frac{P}{4R_{out}}}} \right)}} \right)}} + \theta_{{bend}\text{-}{out}}} \right\}} \right\rbrack}} & \left( {2\text{-}41} \right) \\{\theta_{{out}\text{-}\max} = {\sin^{- 1}\left\lbrack {\frac{n_{g}}{n_{air}}\sin\left\{ {\theta_{{bend}\text{-}{out}} + {\sin^{- 1}\left( {\frac{n_{1}}{n_{g}}\sin\quad\theta_{{NA}\quad 0}} \right)}} \right\}} \right\rbrack}} & \left( {2\text{-}42} \right)\end{matrix}$

In the models shown in FIGS. 34 to 39, it is assumed that the lengths ofthe plurality of layers are equivalent. In this case, the incident lightis not diffused, and only the outgoing direction is converted. On theother hand, in the present invention, the lengths of the individuallayers can be varied. In this case, by varying the outgoing direction ofthe light which goes out from the layer for each layer, the light can bediffused while converting the direction of conversion of the incidentlight.

There may exist various types of the optical waveguide of the typehaving a distribution of refractive indexes which brings out alight-collecting property in the direction of the layer thickness otherthan those having a parabola-shaped distribution of refractive indexesas the gradient index type, such as those having a substantiallytrapezoidal distribution of refractive indexes as shown in FIG. 40. Inany cases, as long as they can propagate the incident light within thelayer, the same outgoing direction converting characteristics as in thecase of the gradient index type can be obtained.

Here, the radius of curvature is not necessarily required to be constantfrom the entrance to the exit of the waveguide both for the step indextype and the type having a distribution of refractive indexes whichbrings out a light-collecting property in the direction of the layerthickness. In the case of a gradual change such that the averageinclination angle of the waveguide is less than 0.01 deg./μm as well,the same light outgoing direction converting effects can be obtained. Inthe case of an abrupt change such that the angle of layer inclination is0.01 deg./μm or higher in the step index type, the light-outgoingdirection converting/diffusing diffusion film of the step index type isobtained as described above. In the case in which the layer inclinationangle is rapidly changed by 0.01 deg./μm or more in the type having adistribution of refractive indexes which brings out a light-collectingproperty in the direction of the layer thickness, a light-outgoingdirection converting/diffusing film having a later-described “astructure in which the step index type and the type having adistribution of refractive indexes which brings out a light-collectingproperty in the direction of the layer thickness are fused” is obtained.

Both in the step index type shown in FIG. 23 and the type having adistribution of refractive indexes which brings out a light-collectingproperty in the direction of the layer thickness shown in FIG. 25, theadjacent layers are in contact with each other in the drawing. However,even though the adjacent layers are separated by some extent, they canbe treated as those having the adjacent layers in contact with eachother. In this case, however, the outgoing direction convertingefficiency may be slightly lowered.

In the case in which the optical waveguide array of the step index typeand the optical waveguide array of the type having a distribution ofrefractive indexes which brings out a light-collecting property in thedirection of the layer thickness are mixed in the direction of thethickness in the light outgoing direction converting film (FIG. 26-a),or in the case in which the optical waveguide array of the step indextype and the optical waveguide array of the type having a distributionof refractive indexes which brings out a light-collecting property inthe direction of the layer thickness are mixed in the direction in afilm plane or in the planar direction in the light-outgoing directionconverting/diffusing film (FIG. 26-b), or in the case of the opticalwaveguide array having a structure in which both of the types are fused,the incident angle range and the outgoing angle range can be obtained byoverlapping the derived results for each type.

[NA Matching with the Optical Engine]

Subsequently, an NA matching between the light-outgoing directionconverting film or the light-outgoing direction converting/diffusingfilm (hereinafter, referred to as the film of the present invention)which constitutes the screen of the present invention and the opticalengine will be described.

A screen aperture angle θ_(S) is defined as θ_(S)≡θ_(S-max)−θ_(S-min)using the minimum aperture angle of screen θ_(S-min) and the maximumaperture angle of screen θ_(S-max). In order to convert thelight-outgoing direction of the projector to the direction of theobserver by matching with the NA of the optical engine, θ_(S) must be atleast 2θ₂ in FIG. 22 and FIG. 27. In other words, from theabove-described expressions (0-1), (0-2) and (0-3), a condition isrepresented as follows.θ_(S)≧tan⁻¹{(1₂ +d/2)/b}−tan⁻¹{(l ₂ +d/2)/b}  (0-4)

Here, the case of the equal sign corresponds to the matched state. Theabove-described θ_(S-min) and θ_(S-max) are respectively equal to thelower limit θ_(in-min) and the upper limit θ_(in-max) of the incidentangle range of the film of the present invention. These values may beobtained by the expressions (1-17) and (1-18) in the case of the stepindex type, and by (2-39), (2-40) in the case of the gradient indextype.

When the optical waveguide array of the step index type and the opticalwaveguide array of the type having a distribution of refractive indexeswhich brings out a light-collecting property in the direction of thelayer thickness are mixed, preferably, the smaller one of the upperlimits of the incident angle ranges of both types is employed as theO_(S-max), and the larger one of the lower limits of the incident angleranges of both types is employed as the O_(S-min). In other words,assuming that the lower limit and the upper limit of the incident anglerange of the optical waveguide of the step index type are θ_(STEPin-min)and θ_(STEPin-max), and the lower limit and the upper limit of theincident angle range of the optical waveguide of the type having adistribution of refractive indexes which brings out a light-collectingproperty in the direction of the layer thickness are θ_(GRADin-min) andθ_(GRADin-max), it is preferable to design the film so as to satisfy thefollowing expression.Min{(θ_(STEPin-max),θ_(GRADin-max)}−Max{(θ_(STEPin-min),θ_(GRADin-min)}≧tan⁻¹{(1₂+d/2)/b}−tan ⁻¹{(1₂ −d/2)/b}  (0-5)

Although the discussion thus far is ideal that utilizes the projectorlight effectively, at least 50% of the light emitted from the opticalengine in the numerical aperture NA must be enter into the screen fromthe range between θ_(min) and θ_(max) in the actual rear projectiondisplay as well.

[Method of Manufacturing the Film of the Present Invention]

Subsequently, a method of manufacturing a diffusion film used in Claims1 to 7 will be described.

This diffusion film is obtained by irradiating light to a mixtureincluding at least two or more different types of photo-polymerizablemonomer or oligomer having different refractive indexes from twodifferent directions for curing the same. The conditions of theirradiation of the light are adequate conditions which satisfy therequirements of the present invention, and the adequate conditions aredetermined by an experiment.

The photo-polymerizable monomer or oligomer is monomer or oligomerhaving at least one polymerizable group such as acryloyl group,metaacryloyl group, or vinyl group in a particle. A mixture of aplurality of chemical compounds is applied on the substrate orencapsulated in the cell to obtain a film and cured gradually whileirradiating light from two or more directions.

The light to be irradiated may have any wavelength as long as it cancure the compound which includes monomer or oligomer, and visible lightbeam or ultraviolet beam are often used.

The ultraviolet beam is irradiated by using a mercury lamp or a metalhalide lamp or the like. However, when a rod-shaped lamp is used, byadjusting the conditions of irradiation, the obtained sheet like curedsubstance is caused to have anisotropy between the longer axis and theshorter axis of a light source, so that the light is diffused only whenbeing rotated about the longer axis of the light source.

The lights from two or more directions are used for changing theincident angle of the light with respect to the surface of the sample tobe cured for curing. If the difference of the angle of light coming fromthe adjacent two light sources onto the sample is 50° or larger, theangular range of diffusion of the diffusion film become narrower.Therefore, the angle is preferably within 50°, and more preferably,within 30°.

Subsequently, a method of manufacturing a film having a curved waveguidearray structure used in Claims 8 to 14 of the present invention will bedescribed.

The film is obtained by manufacturing a waveguide structure which is notcurved by irradiating light onto a mixture of at least two types ofphoto-polymerizable monomer or oligomer having different refractiveindexes for curing the same, and physically bending the same.

The photo-polymerizable monomer or oligomer is monomer or oligomerhaving at least one polymerizable group such as acryloyl group,metaacryloyl group, vinyl group in a particle. A mixture of a pluralityof chemical compounds is applied on the substrate or encapsulated in thecell to obtain a film and cured gradually while irradiating light.

The light to be irradiated may have any wavelength as long as it cancure the compound which includes monomer or oligomer, and, for example,visible light beam or ultraviolet beam is often used.

The ultraviolet beam is irradiated by using a mercury lamp or a metalhalide lamp or the like. However, when a rod-shaped lamp is used, byadjusting the conditions of irradiation, the obtained sheet like curedsubstance is caused to have anisotropy between the longer axis and theshorter axis of the light source, so that the light can be diffused onlywhen being rotated about the longer axis of a light source.

The film generated in this manner has a structure in which the opticalwaveguide of the step index type and the optical waveguide of the typehaving a distribution of refractive indexes which brings out alight-collecting property in the direction of the layer thickness fusedwith each other.

By soaking the film in an organic solvent to soften and applying aphysical force to curve the waveguide structure which has not beencurved, the film having a curved waveguide array structure used Claims 8to 16 of the present invention is obtained. The organic solvent may beof any type as long as it can soften the film without impairing thestructure of the waveguide of the film.

First Embodiment

The diffusion film used in a first embodiment corresponds to the film(1), and as shown in FIG. 20, it is divided into the incident sideportion and the outgoing side portion in structure. In the incident sideportion is formed of layer array which corresponds to the opticalwaveguide of the step index type, in which the difference between therefractive indexes n₁ and n₂ of the two types of layers laminatedalternately in the y-direction is relatively small, and fluctuations inthe layer inclination angle is large. On the other hand, the outgoingside portion is formed of layer array which corresponds to the opticalwaveguide of the step index type in which the difference between therefractive indexes n₁ and n₂ of the two types of layers laminatedalternately in y-direction is relatively large, there are littlefluctuations in the layer inclination angle, and the layer inclinationangle is −3° with respect to the normal line to the film. The diffusionfilm has values y_(max)=4 μm and L=300 μm, which satisfies therequirement in Claim 3, (L≧10×y_(max)).

The refractive indexes of the incident side portion are n₁=1.5325,n₂=1.5275, and the difference in refractive indexes Δn=n₁−n₂=0.005. Thedistribution of the layer inclination angle includes two factors; firstcomponents being fluctuated substantially uniformly between 0° and+6.5°, and second components which exist at 0° intensively as an exampleof the measurements shown in FIG. 13 and summary shown in FIG. 20. A“frequency” of the layer inclination angle in FIG. 13 and FIG. 20corresponds to the “existential probability” described above. The firstcomponents realize the diffusion characteristics of the top hat type,and the second components form a peak of the measurements.

When the values of θ₁′, θ₁″, θ₂′ and θ₂″ are calculated by substitutingthe values for the parameters in the incident side portion, that is,θ+Δθ_(max)=6.5°, θ−Δθ_(max)=0°, n₁=1.5325, n₂=1.5275 in the expressions(1) to (4) which express the diffusion characteristics, θ₁′=17.2°,θ₁″=7.11°, θ₂′=2.87°, and θ₂″=−7.11° are obtained. Therefore, from theexpression (5), the angular range of diffusion of the outgoing lightθ_(out) of this incident side portion is; −7.11°≦θ_(out)≦17.2°.Therefore, the light incoming within the range of −7.11°≦θ_(in)≦17.2°diffused substantially uniformly within the range of−7.11°≦θ_(out)≦17.2° due to the first components.

Subsequently, this light enters into the layer array of the outgoingside portion. The refractive indexes of the outgoing side portion aren₁=1.55, n₂=1.51, the difference in refractive index is Δn=n₁−n₂=0.04,and the layer inclination angle is −3°. Therefore, there are littlefluctuations.

The light diffused substantially uniformly within the range of−7.11°≦θ_(out)≦17.2° in the incident side portion is caught by theoptical waveguide of the step index type having the value n₁=1.55, whichconstitutes the outgoing side portion, and repeats the multiplereflections. The light assumes a uniformly diffused light of−4.58°≦θ_(in)≦11.0° within the outgoing side portion, and the layerinclination angle is −3°. Therefore, the lights within the angular rangeof −4.58°≦θ_(in)≦−3° and −3≦θ_(in)≦11.0° repeat total reflectionssymmetrically about −3° as a center. However, the angular range of thelight that allows total reflection in the angular range of−3°≦θ_(in)≦11.0° is the light within the range −3°≦θ_(in)≦10.0° sincen₁=1.55, n₂=1.51. Therefore, the light is diffused substantiallyuniformly within the angular range of −16.0°≦θ_(in)≦11.0° inside theoutgoing side portion. When the light within this range goes out intothe air layer, the light diffuses substantially uniformly within theangular range of −25.4°≦θ_(out)≦17.2°. This substantially coincides withthe measurements.

Subsequently, the peak of the light will be analyzed. Since the peak offrequency exists at the point of 0° in the distribution of the layerinclination angle in the incident side portion, when the light enters atthe angle of 0°, this incident angle travels through the incident sideportion at the angle of 0° by the influence of the peak. When thistraveled light enters into the outgoing side portion, it is totallyreflected in the layer at −3°. Therefore, this light travels in thedirection of −6° when it is reflected by an odd number of times and inthe direction of 0° when it is reflected by an even number of times.Consequently lights of 0° and −6° are generated. When these lights goout into the air layer, they travel in the directions of 0° and −9.32°,and hence, the peaks are generated at 0° and −9.32° in the measurements.

Second Embodiment

The diffusion film used in the second embodiment corresponds to the film(3) and, as shown in FIG. 21, is divided into the incident side portionand the outgoing side portion in structure. The incident side portion isformed of the layer array of the gradient index type, and the outgoingside portion is formed of the layer array of the step index type.Although this diffusion film is the same as that in the first embodimentby itself, in the second embodiment, the incident side portion of thediffusion film is also applicable to the model of the above-describedgradient index type, and the fact that the diffusion characteristics canbe described satisfactorily with this model is shown.

In the layer array in the incident side portion, the optical axes of thewaveguides are fluctuated as shown in a measurement example in FIG. 13.The term “the optical axes are fluctuated” means that angles formedbetween the optical axes and the normal line of the film plane(corresponds to the angle of layer inclination in FIG. 13) arefluctuated. The refractive index distribution function of within eachwaveguide is a parabolic distribution function shown by the expression(6), and the parameters are b₁=2 μm, n₁=1.5325, and n₂=1.5275.Therefore, A=6.525×10⁹ is obtained from the expression (9), andP/2=38.89 μm is obtained from the expression (8). Since fluctuations ofthe optical axes are within the range between 0° and 6.5°, theexpression (7) may be established when θ=0°, that is,L_(zmax)=L_(zmin)≧38.89 μm. In this embodiment, L_(zmax)−L_(zmin) is onthe order of 40 μm as shown in FIG. 21, the incident light can bediffused uniformly. Although the optical axes are fluctuated in therange between 0° and 6.5° in the diffusion film in this embodiment, thewaveguides which determine the edge portion of having the diffusioncharacteristics of the top hat type are the waveguides at 0° and 6.5°,and hence the analysis will be made for 0° and 6.5°.

The wave guide at 6.5° will be analyzed first. In the waveguide, thelight meandering within the range obtained by the expression (15).Therefore, the angle of diffusion by this waveguide is from −0.557° to13.56°. When it is assumed that n₁=n_(g) is established, this diffuselight enters into the layer array of the step index type whichconstitutes the outgoing side portion. The parameters on the outgoingside are: n₁=1.55, n₂=1.51, and the difference of refractive index Δn=n₁−n₂=0.04, and the layer inclination angle is −0.3°. Therefore, thereare little fluctuations.

The light which is uniformly diffused within the range between −0.557°and 13.56° in the incident side portion is caught by the opticalwaveguide of the step index type of n₁=1.55 on the outgoing sideportion, and repeats the multiple reflections. Within the outgoing sideportion, the light is converted into the uniform diffuse light in therange between −0.551° and 13.4°, and the layer inclination angle is −3°.Therefore, the light repeats the total reflections symmetrically about−3° as a center. However, the angular range of the light that allowstotal reflection in the angular range between −0.551° and 13.4° is onlythe angular range between −0.551° and 10° since n₁=1.55, and n₂=1.51.Therefore, the light is diffused within the angular ranges between−16.0° and −5.45°, and −0.551° and 13.4° uniformly inside the portion ofthe outgoing side. Although there is no light in the range between−5.45° and −0.551°, since the optical waveguides of the gradient indextype of 0° to 6.5° fill therein, the light is diffused uniformly withinthe angular range between −16° and 13.4°. When this light is emitted tothe air layer, the light is diffused within the angular range between−25.4° and 21.1° uniformly.

When the case in which the waveguide of the gradient index type in theincident side portion is 0° is analyzed in the same manner, the lightemitted from the outgoing side portion diffuses uniformly within theangular range between −20.4° and 10.9°. Therefore, the light is diffuseduniformly in the angular range between −25.4° and 21.1° with thelamination model including the incident side portion composed of thelayer array of the optical waveguides of the gradient index type whoseoptical axes are fluctuated in the range between 0° and 6.5° and theoutgoing side portion composed of the layer array of the opticalwaveguides of the step index type which are included in the rangebetween −25.4° to and 21.1°.

Subsequently, the peak of the light will be analyzed. Since the peak offrequency exists at the point of 0° in the fluctuation distribution ofthe optical axes of the waveguides in the incident side portion, ifthere is a gap between the waveguides at 0°, part of light may gothrough. When the incident angle is 0°, this light passes through as isto the outgoing side portion. Since the layers on the outgoing sideportion are inclined by −3°, the light is totally reflected on the layerof −3°, and if it is reflected by the odd number of times, it travels tothe direction of −6°, and when it is reflected by the even number oftimes, it travels to the direction of 0°, and hence the light of 0° andthe light of −6° are generated. When these lights go out to the airlayer, it travels to the direction of 0° and −9.32°, and hence the peaksare generated at 0° and −9.32° in the measurement.

Third Embodiment

In a third embodiment, as shown in FIG. 41 (a), a structure which isoptically equivalent to the curved waveguide structure of thelight-outgoing direction converting/diffusing film used in the presentinvention is obtained by arranging an optical film strip 9A obtainedfrom an optical film 9 having a structure in which layers 91 and layers92 are arranged in piles alternately in the direction of the planerhaving different refractive indexes in a bent manner as shown in FIG.41(b). The thickness of each layer is 2 μm. The respective layer has astructure including the optical waveguide of the step index type inwhich the radius of curvature of the layer interface is locally variedand the optical waveguide of the gradient index type in which the lengthof the layer is varied fused with each other, and the refractive indexat the center of the layer thickness is 1.55 in the layer 9 ₁ and is1.51 in the layer 9 ₂. In order to prevent total reflection on the airinterface, as shown in FIG. 41(b), the periphery of the bent opticalfilm strip 9A is filled with transparent medium 12 having refractiveindex of 1.6. The radius of curvature is 4 cm for the minimum layer,which is sufficiently larger than either of the R_(minstep) of theexpression (1-16) and the R′_(min) of the expression (2-32).

An experiment to cause light (incident light 11 ₁) to be entered intothe optical film strip 9A arranged in a curved state as described abovefrom the side of one end surface using a light source 11 is conducted,and the fact that the light goes out from the side of the other endsurface as an outgoing light 11 ₂ is confirmed. The intensity of theoutgoing light 11 ₂ is substantially the same as the intensity of theincoming light 11 ₁.

Fourth Embodiment

In a fourth embodiment, a detailed example of a design in which the NAmatching between the light-outgoing direction converting film and theoptical engine is performed in the case in which the screencorresponding to Claim 8 (the light-outgoing direction converting filmof the step index type+diffusing film) is applied to the actualthin-type rear projection display system shown in FIG. 33.

The optical system deployed with the mirrors M1, M3 and thenon-spherical mirror M2 of the actual system removed is as shown in FIG.27.

In the actual system, as shown in FIG. 33, the light changes thedirection three times by the mirrors M1, M2 and the non-spherical mirrorM2 on the backside of the screen 10, and the output light from theoptical engine 20 is bent traversely by the mirror M1 which is locatedimmediately in front toward the side. Assuming that the depth of theactual system (a distance between the surfaces of the mirror M3 and thescreen 10) is 20 cm, the height of the screen 10 is 1 m, and thedistance between the centers of the lens and the mirror M1 is 40 cm,b=20 cm×3+40 cm =1 m, S₂=1 m in the deployed optical system in FIG. 27.Assuming that the vertical length of an image display panel 21 (=S₁ inFIG. 27) including the DMD chip is 2.5 cm, a=2.5 cm from themagnification S₂/S₁=1 m/2.5 cm =40=b/a=1 m/a, and the focal distance fof the lens is f=2.44 cm from 1/a+1/b=1/f. A lens diameter d is 2.4 cm.When l₁=30 cm, l₂=l₁+S₂=130 cm.

Since a parameter of the optical system is now determined, from theexpressions (0-2) and (0-3), θ₁ and θ₀ in FIG. 27 is θ₁=52.474° andθ₀=16.066°. The range of the angle θ_(opt) which determines the outputNA of the optical system is between θ₀ and θ₁ inclusive. When this rangematches the range of the incoming angle of the light-outgoing directionconverting film, the NA matching is achieved.

Since the range of the input angle of the light-outgoing directionconverting film of the step index type is between θ_(in4) and θ_(in5)inclusive from the expression (1-12), the conditions of achievement ofthe NA matching is θ_(in4)=θ₀=16.066°, θ_(in5)=θ₁=52.474°.

Subsequently, θ_(bend) (corresponds to θ_(bend-in)) will be calculated.θ_(bend) is calculated by the following expression which is derived froman expression derived by substituting +θ_(in4) for −θ_(in4) in theexpression (1-9), and the expression (1-11).θ_(bend)=½×[sin⁻¹(n _(air) /n _(g)×sin θ_(in4))+sin⁻¹(n _(air) /n_(g)×sin θ_(in5))]  (1-21)

When calculating by substituting the respective values described abovefor θ_(in4) and θ_(in5), and assuming n_(g)=1.5 and n_(air)=1.0,θ_(bend)=21.275° is obtained.

Subsequently, the radius of curvature of the bent waveguide iscalculated. In this calculation, r₀ is calculated by entering the valuesof θ_(in5), θ_(bend), n_(g), n_(air), n₁, n₂, y₁ (width of the opticalwaveguide=layer thickness) in the following expression:sin[cos⁻¹ {n _(g) /n ₁×sin(sin⁻¹(n _(air) /n _(g)×sinθ_(in5))−θ_(bend))}]=n ₂ /n ₁×(1+y ₁ /r ₀)  (1-11B)

which is obtained by modifying the expression (1-11), and, fromR=r₀+y₁/2, the radius of curvature is obtained. When the r₀ is obtainedassuming that the θ_(in5), θ_(bend), n_(g), n_(air) are theabove-described respective values, and that n₁=1.55, n₂=1.51, y₁=4 μm,r₀=401.617 μm is obtained. Therefore, the radius of curvature isrepresented by R=r₀+y₁/2=403.617 μm.

When θ_(bend) is used, since the thickness t_(f) of the film is(r₀+y₁)×sin θ_(bend) from FIG. 42, and hence the expressiont_(f)=(r₀+y₁)×sin θ_(bend)=147.2 μm is established.

On the other hand, since the NA on the outgoing side is determined bythe expression (1-5), when the r₀ and other parameters obtained aboveare substituted into the expression (1-5), θ_(out2)=16.084° is obtained.Therefore, from the expression (1-6), the angular range that determinesthe NA on the output side becomes −16.084°≦θ_(NAstep)≦+16.084°.

Fifth Embodiment

In a fifth embodiment, a detailed example of a design in which the NAmatching between the light-outgoing direction converting film and theoptical engine is performed in a case in which the screen correspondingto Claim 9 (gradient index type light-outgoing direction convertingfilm+diffusing film) is applied to the thin-type rear projection displaysystem which is the same as in the fourth embodiment will be described.

The range of the angle θ_(opt) which determines the output NA of theoptical system is between θ₀(=16.066°) and θ₁ (=52.474°) inclusive as inthe case of the forth embodiment. When this range matches the inputangular range of the light-outgoing direction converting film, the NAmatching is achieved.

The input angular range of the light-outgoing direction converting filmof the gradient index type is, from the expression (2-16A), betweenθ_(in1) and θ_(in2) inclusive. Therefore, the conditions of achievementof the NA matching is θ_(in2)=θ₀=16.066°, θ_(in1)=θ₁=52.474°.

Subsequently, θ_(bend) (corresponds to θ_(bend-in)) is calculated.θ_(bend) is calculated by the following expression which is obtained bymodifying the expression (2-12A).θ_(bend)=sin⁻¹(n _(air) /n _(g)×sin θ_(in1))−sin⁻¹(n ₁ /n _(g)×sinθ_(NA0))  (2-12B)

Here, θ_(NA0) is calculated by the expression (2-5):θ_(NA0)=tan⁻¹(n₁×√A×y₁/2), and the A in the expression (2-5) iscalculated by the expression (2-2): A=(8/y₁ ²)×(n₁−n₂)/n₁.

When 4 μm is substituted for y₁, 1.55 is substituted for n₁, and 1.51 issubstituted for n₂ in the expression (2-2), A=1.290×10¹⁰ is established.When the value A and the above-described y₁, n₁ values are substitutedinto the expression (2-5), θ_(NA0)=19.397° is established. Therefore,the value of θ_(NA0), the θ_(in1), the value of n₁, n_(g)=1.5,n_(air)=1.0 are substituted into the expression (2-12B), so thatθbend=11.848° is determined.

Subsequently, the value n is determined. The value n is calculated usingthe following expression obtained by modifying the expression (2-15A).n=θ _(NA0)/[θ_(NA0)−sin⁻¹ {n _(g) /n ₁×sin{θ_(bend)−sin⁻¹(n _(air) /n_(g)×sin θ_(in2))}}]  (2-15B)

The respective values corresponding to the parameters in the expressionis substituted into the expression (2-15B), so that n=1.0646 isdetermined.

Then, the radius of curvature of the bent waveguide is calculated. Inthis calculation, the value A is substituted into the expression (2-4):P=2×π/√A to obtain P=55.32 μm, and then the value P, the value ofθ_(NA0), and the value n are substituted into the expression (2-30):R=r₀+y₁/2=(P/4)/tan (θ_(NA0)/(2×n)), so that the radius of curvatureR=86.247 μm is determined.

From FIG. 42, since the thickness t_(f) of the film is (r₀+y₁)×sinθ_(bend), when using θ_(bend), t_(f)=(r₀+y₁)×sin θ_(bend)=18.1185 μm(when θ_(bend-out)=0°).

On the other hand, the NA on the output side is designed by the outputsymmetry on the upper and lower sides. The angle of the optical axis onthe output side θ_(axis) (=θ_(bend-out)) is obtained by substituting therespective values corresponding to the parameters in the expression(2-26), which is θ_(axis) (=θ_(bend-out))=9.4273°. Therefore, from theexpression (2-27), θ′_(out3)=θ′_(out4)=16.084°. Therefore, from theexpression (2-28), the range of the angle which determines the output NAwhich is symmetry on the upper and lower side of the light-outgoingdirection converting film is −16.084°≦θ_(NAout)≦16.084°.

INDUSTRIAL APPLICABILITY

The present invention can be used for designing and manufacturing therear (or front) projection display screen.

1-16. (canceled)
 17. A projection display screen having a diffusion filmfor diffusing light incoming from an angular range of diffusion of anincident light into an angular range of diffusion of an outgoing light,wherein the diffusion film comprises a structure in which a plurality oflayers, each of which has a different refractive index from the adjacentlayers, constituting a plurality of optical waveguides of a step indextype forms stripes arranged in the banded state in a direction in a filmplane and extends in the direction of the layer inclination angledistributed substantially in a top hat shape within a predeterminedangular range with respect to the direction of the film thickness.
 18. Aprojection display screen having a diffusion film for diffusing lightincoming from an angular range of diffusion of an incident light into anangular range of diffusion of an outgoing light, wherein the diffusionfilm comprises a structure in which a plurality of layers, each of whichhas a different refractive index from the adjacent layers, constitutinga plurality of optical waveguides of a step index type forms stripesarranged in the banded state in a direction in a film plane, one or morepeaks are included within a predetermined angular range with respect tothe direction of the film thickness, and the plurality of layers extendsin the direction of the layer inclination angle distributedsubstantially in a top hat shape excepting said peaks excepting saidpeaks within the angular range.
 19. The projection display screenaccording to claim 18, wherein the structure of the diffusion filmincludes a film thickness L and a maximum value of the width of thestrip y_(max) which satisfy the following expression:L≧10×y _(max)
 20. The projection display screen according to claim 18,wherein the structure of the diffusion film includes a film thickness Land a maximum value of the width of the strip y_(max) which satisfy thefollowing expression:L≧10×y _(max)
 21. A projection display screen having a diffusion filmfor diffusing light incoming from an angular range of diffusion of anincident light into an angular range of diffusion of an outgoing light,wherein the diffusion film comprises a structure in which a plurality oflayers constituting optical wave guides having a refractive indexdistribution that brings out a light-collecting property in thedirection of the layer thickness extends in the direction of the filmthickness or in the direction inclined from this direction with a layerlength distributed within a predetermined range substantially in the tophat shape in a portion in the direction of the film thickness.
 22. Theprojection display screen according to claim 21, wherein the structureof the diffusion film has the refractive index distribution of theoptical waveguides is of a gradient index type, and a layer inclinationangle θ, a maximum value L_(zmax) and a minimum value L_(zmin) of thelayer length, and a pitch P of the optical waveguides satisfy thefollowing expression;L _(zmax) −L _(zmin)≧(P/2)×cos θ
 23. A screen using a film having afunction of converting a light-outgoing direction comprising a diffusionfilm for diffusing light incoming from an angular range of diffusion ofthe incident light into an angular range of diffusion of an outgoinglight; and a light-outgoing direction converting film for causing lightincoming from an oblique direction to go out toward the front, whereinthe light-outgoing direction converting film comprises a structure inwhich a plurality of layers, each of which has a different reflectiveindex from the adjacent layers, forming a plurality of step index typeoptical waveguides is arranged in a banded state in the direction in afilm plane, and extends so as to be bent with respect to the directionof the film thickness.
 24. A screen using a film having a function ofconverting a light-outgoing direction comprising a diffusion film fordiffusing light incoming from an angular range of diffusion of theincident light into an angular range of diffusion of an outgoing light;and a light-outgoing direction converting film for causing lightincoming from an oblique direction to go out toward the front, whereinthe light-outgoing direction converting film comprises a structure inwhich a plurality of layers forming optical waveguides having adistribution of refractive indexes which brings out a light-collectingproperty in the direction of the layer thickness is arranged in a bandedstate in the direction in a film plane, and extend so as to be bent withrespect to the direction of the film thickness.
 25. A screen using afilm having a function of converting a light-outgoing directioncomprising a diffusion film for diffusing light incoming from an angularrange of diffusion of the incident light into an angular range ofdiffusion of an outgoing light; and a light-outgoing directionconverting film for causing light incoming from an oblique direction togo out toward the front, wherein the light-outgoing direction convertingfilm comprises a structure in which the structure according to claim 23and a structure in which a plurality of layers forming opticalwaveguides having a distribution of refractive indexes which brings outa light-collecting property in the direction of the layer thickness isarranged in a banded state in the direction in a film plane, and extendso as to be bent with respect to the direction of the film thickness aremixed in one or both of the film thickness direction and in thedirection in the film plane.
 26. The screen using a film having afunction of converting a light-outgoing direction according to claim 23,wherein the angular range of diffusion of the incident light of thediffusing film matches the outgoing angular range of the light-outgoingdirection converting film.
 27. A screen having a light-outgoingdirection converting/diffusing film that causes incident light from anoblique direction to diffuse and go out toward the front direction,wherein the light-outgoing direction converting/diffusing film comprisesa structure in which a plurality of layers, each of which has differentrefractive index from the adjacent layers, and forming a plurality ofstep index type optical waveguides is arranged in a banded state in thedirection in a film plane, and extends so as to be bent with respect tothe direction of the film thickness, and layer inclination angles aredistributed substantially in a top hat shape.
 28. A screen having alight-outgoing direction converting/diffusing film that causes incidentlight from an oblique direction to diffuse and go out toward the frontdirection, wherein the light-outgoing direction converting/diffusingfilm comprises a structure in which a plurality of layers formingoptical waveguides having a distribution of refractive indexes whichbrings out a light-collecting property in the direction of the layerthickness is arranged in a banded state in the direction in a filmplane, and extends so as to be bent with respect to the direction of thefilm thickness, and the length of the layers are distributedsubstantially in a top hat shape.
 29. The screen having a light-outgoingdirection converting/diffusing film that causes incident light from anoblique direction to diffuse and go out toward the front direction,wherein the light-outgoing direction converting/diffusing film comprisesa structure (A) in which the structure according to claim 28 and astructure (B) in which a plurality of layers forming optical waveguideshaving a distribution of refractive indexes which brings out alight-collecting property in the direction of the layer thickness isarranged in a banded state in the direction in a film plane, and extendsso as to be bent with respect to the direction of the film thickness,and the length of the layers are distributed substantially in a top hatshape are mixed in one or both of the film thickness direction and inthe direction of the film plane, or the structure (A) and the structure(B) are fused with each other.
 30. An optical system for projectiondisplay system comprising a screen using a film having a function ofconverting a light-outgoing direction according to claim 23; a projectorwhich emits an incident light to the screen, wherein a projectoraperture and arrangement of the projector matches an angular range ofincidence of the screen.
 31. The optical system for projection displaysystem comprising a screen using a film having a function of convertinga light-outgoing direction according to claim 26; a projector whichemits an incident light to the screen, wherein a projector aperture andarrangement of the projector matches an angular range of incidence ofthe screen.
 32. The optical system employing projection display systemaccording to claim 30, further comprising a reflection mirror whichreflects the emitted light from the projector and causes the same toenter the screen, wherein the arrangement of the reflection mirrormatches the angular range of incidence of the screen.
 33. The opticalsystem employing projection display system according to claim 31,further comprising a reflection mirror which reflects the emitted lightfrom the projector and causes the same to enter the screen, wherein thearrangement of the reflection mirror matches the angular range ofincidence of the screen.